Publications by Anthony W. Knapp

NOTICE:  The PDF files of articles on this webpage are intended only for nonprofit educational and scientific purposes.  Their inclusion here is to expedite the traditional colleague-to-colleague sharing of individual reprints and preprints of papers.  Downloading of these papers for any other purpose may run afoul of the rights of a publisher under the copyright law.

Below is a list of my publications—books, articles, and other writing.

Skip to: 1964 | 1970 | 1975 | 1980 | 1985 | 1990 | 1995 | 2000 | 2005 | 2010 | Book reviews | Other writing.


Books and articles
  1. Distal functions, Proceedings of the National Academy of Sciences of the USA 52 (1964), 1409-1412.
    Reprint in PDF.

  2. Connection between Brownian motion and potential theory, Journal of Mathematical Analysis and Applications 12 (1965), 328-349.
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  3. Regular boundary points in Markov chains, Proceedings of the American Mathematical Society 17 (1966), 435-440.
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  4. (with J. G. Kemeny and J. L. Snell) Denumerable Markov Chains, D. Van Nostrand Co., Inc., Princeton, New Jersey, 1966.
    Access to the front matter.

  5. Decomposition theorem for bounded uniformly continuous functions on a group, American Journal of Mathematics 88 (1966), 902-914.
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  6. Distal functions on groups, Transactions of the American Mathematical Society 128 (1967), 1-40.
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  7. Fatou's theorem for symmetric spaces I, Annals of Mathematics 88 (1968), 106-127.
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  8. Doubly generated Fuchsian groups, Michigan Mathematical Journal 15 (1968), 289-304.
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  9. Functions behaving like almost automorphic functions, Topological Dynamics, an International Symposium, J. Auslander and W. Gottschalk (ed.), W. A. Benjamin Inc., New York, 1968, pp. 299-317.
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  10. (with P. J. Kahn) Equivariant maps onto minimal flows, Mathematics Systems Theory 2 (1968), 319-324.
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  11. (with E. M. Stein) Singular integrals and the principal series, Proceedings of the National Academy of Sciences of the USA 63 (1969), 281-284.
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  12. (with E. M. Stein) The existence of complementary series, Problems in Analysis, a Symposium in Honor of Salomon Bochner, R. C. Gunning (ed.), Princeton University Press, Princeton, New Jersey, 1970, pp. 249-259.
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  13. (with E. M. Stein) Singular integrals and the principal series II, Proceedings of the National Academy of Sciences of the USA 66 (1970), 13-17.
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  14. (with E. M. Stein) Intertwining operators for semisimple groups, Annals of Mathematics 93 (1971), 489-578.
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  15. (with R. E. Williamson) Poisson integrals and semisimple groups, Journal d'Analyse Mathématique 24 (1971), 53-76.
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  16. (with E. M. Stein) Irreducibility theorems for the principal series, Conference on Harmonic Analysis, Lecture Notes in Mathematics 266 (1972), Springer-Verlag, New York, pp. 197-214.
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  17. Bounded symmetric domains and holomorphic discrete series, Symmetric Spaces, W. M. Boothby and G. L. Weiss (eds.), Marcel Dekker Inc., New York, 1972, pp. 211-246.
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  18. (with K. Okamoto) Limits of holomorphic discrete series, Journal of Functional Analysis 9 (1972), 375-409.
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  19. Determination of intertwining operators, Harmonic Analysis on Homogeneous Spaces, Proceedings of Symposia in Pure Mathematics 26 (1973), American Mathematical Society, Providence, Rhode Island, pp. 263-268.
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  20. Commutativity of intertwining operators, Bulletin of the American Mathematical Society 79 (1973), 1016-1018.
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  21. (with R. Harvey) Positive (p,p) forms, Wirtinger's inequality, and currents, Value Distribution Theory, Part A, R. O. Kujala and A. L. Vitter (eds.), Marcel Dekker Inc., New York, 1974, pp. 43-62.
    Reprint in PDF.

  22. (with E. M. Stein) Singular integrals and the principal series III, Proceedings of the National Academy of Sciences of the USA 71 (1974), 4622-4624.
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  23. A Szegö kernel for discrete series, Proceedings of the International Congress of Mathematicians, 1974, 2 (1975), Canadian Mathematical Congress, 99-104.
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  24. Weyl group of a cuspidal parabolic, Annales Scientifiques de l'Ecole Normale Supérieure 8 (1975), 275-294.
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  25. (with E. M. Stein) Singular integrals and the principal series IV, Proceedings of the National Academy of Sciences of the USA 72 (1975), 2459-2461.
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  26. Commutativity of intertwining operators II, Bulletin of the American Mathematical Society 82 (1976), 271-273.
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  27. (with J. G. Kemeny and J. L. Snell) Denumerable Markov Chains, second edition, Springer-Verlag, New York, 1976.
    Access to the front matter.

  28. (with E. M. Stein) Intertwining operators for SL(n,R), Studies in Mathematical Physics, Essays in Honor of Valentine Bargmann, E. H. Lieb, B. Simon, and A. S. Wightman (eds.), Princeton Series in Physics, Princeton University Press, Princeton, New Jersey, 1976, pp. 239-267.
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  29. (with N. R. Wallach) Szegö kernels associated with discrete series, Inventiones Mathematicae 34 (1976), 163-200, and 62 (1980), 341-346.
    Reprint of article in PDF.
    Reprint of correction and addition in PDF.

  30. (with G. Zuckerman) Classification of irreducible tempered representations of semisimple Lie groups, Proceedings of the National Academy of Sciences of the USA 73 (1976), 2178-2180.
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  31. (with G. Zuckerman) Classification theorems for representations of semisimple Lie groups, Non-Commutative Harmonic Analysis, Lecture Notes in Mathematics 587 (1977), Springer-Verlag, New York, pp. 138-159.
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  32. Irreducible tempered representations, Lie Theories and Their Applications, Proceedings of the 1977 Annual Seminar of the Canadian Mathematical Congress, Queen's Papers in Pure and Applied Mathematics, No. 48, Queen's University, Kingston, Ontario, 1978, pp. 487-495.
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  33. Representations of GL$_2(R)$ and GL$_2(C)$, Automorphic Forms, Representations, and $L$-Functions, Proceedings of Symposia in Pure Mathematics 33 (1979), Part 1, American Mathematical Society, Providence, Rhode Island, pp. 87-91.
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  34. (with G. Zuckerman) Normalizing factors, tempered representations, and $L$-groups, Automorphic Forms, Representations, and $L$-Functions, Proceedings of Symposia in Pure Mathematics 33 (1979), Part 1, American Mathematical Society, Providence, Rhode Island, pp. 93-105.
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  35. (with E. M. Stein) Intertwining operators for semisimple groups II, Inventiones Mathematicae 60 (1980), 9-84.
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  36. (with G. Zuckerman) Multiplicity one fails for $\frak p$-adic unitary principal series, Hiroshima Mathematical Journal 10 (1980), 295-309.
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  37. Notes on covering spaces, duplicated notes, Cornell University, Fall 1981.
    Commentary | Original notes in PDF.

  38. (with S. S. Gelbart) Irreducible constituents of principal series of SL$_n(k)$, Duke Mathematical Journal 48 (1981), 313-326.
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  39. (with E. M. Stein) Some new intertwining operators for semisimple groups, Non Commutative Harmonic Analysis and Lie Groups, Lecture Notes in Mathematics 880 (1981), Springer-Verlag, New York, pp. 303-336.
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  40. Letter to David Vogan, Langlands L-classes exist for SU(3,2) that contain a mixture of unitary and nonunitary representations, October 19, 1982.
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  41. (with S. S. Gelbart) $L$-indistinguishability and $R$ groups for the special linear group, Advances in Mathematics 43 (1982), 101-121.
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  42. (with B. Speh) Irreducible unitary representations of $SU(2,2)$, Journal of Functional Analysis 45 (1982), 41-73.
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  43. (with B. Speh) Status of classification of irreducible unitary representations, Harmonic Analysis, Lecture Notes in Mathematics 908 (1982), Springer-Verlag, New York, pp. 1-38.
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  44. Commutativity of intertwining operators for semisimple groups, Compositio Mathematica 46 (1982), 33-84.
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  45. (with G. J. Zuckerman) Classification of irreducible tempered representations of semisimple groups, Annals of Mathematics 116 (1982), 389-501, and 119 (1984), 639.
    Reprint of 1982 article: PDF.
    Reprint of 1984 typesetter's correction: PDF.

  46. Representation Theory of Semisimple Groups, by Examples, preliminary edition, Université Paris VII, Paris, 1982.

  47. Minimal K-type formula, Non Commutative Harmonic Analysis and Lie Groups, Lecture Notes in Mathematics 1020 (1983), Springer-Verlag, New York, pp. 107-118.
    Reprint in PDF.
    Guide to details of proof: HTML.  |  First set of handwritten notes giving proof: PDF.  |  Second set of handwritten notes giving proof: PDF.

  48. (with B. Speh) The role of basic cases in classification: Theorems about unitary representations applicable to SU(N,2), Non Commutative Harmonic Analysis and Lie Groups, Lecture Notes in Mathematics 1020 (1983), Springer-Verlag, New York, pp. 119-160.
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  49. Unitary representations and basic cases, Lie Group Representations I, Lecture Notes in Mathematics 1024 (1983), Springer-Verlag, New York, pp. 77-98.
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  50. Investigations of unitary representations of semisimple Lie groups, Topics in Modern Harmonic Analysis I, Proceedings of a Seminar Held in Torino and Milano May-June 1982, Istituto Nazionale di Alta Matematica Francesco Severi, Rome, 1983, pp. 9-43.
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  51. (with M. W. Baldoni Silva) Indefinite intertwining operators, Proceedings of the National Academy of Sciences of the USA 81 (1984), 1272-1275.
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  52. Langlands classification and unitary dual of $SU(2,2)$, Applications of Group Theory in Physics and Mathematical Physics, M. Flato, P. Sally, and G. Zuckerman (eds.), Lectures in Applied Mathematics 21 (1985), American Mathematical Society, Providence, Rhode Island, pp. 209-217.
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  53. Representation Theory of Semisimple Groups: An Overview Based on Examples, Princeton Mathematical Series 36, Princeton University Press, Princeton, New Jersey, 1986.
    Access to the front matter and a list of corrections.

  54. (with M. W. Baldoni-Silva) Unitary representations induced from maximal parabolic subgroups, Journal of Functional Analysis 69 (1986), 21-120.
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  55. (with D. A. Vogan) Duality theorems in relative Lie algebra cohomology, duplicated notes, SUNY Stony Brook and Massachusetts Institute of Technology, 1986.
    Commentary | Original notes in PDF.

  56. (with M. W. Baldoni-Silva) Indefinite intertwining operators II, Analisi Armonica, Spazi Simmetrici e Teoria della Probabilità, Cortona 2-5 Luglio 1984, Symposia Mathematica 29 (1987), Istituto Nazionale di Alta Matematica Francesco Severi, Rome, pp. 1-44.
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  57. (with M. W. Baldoni-Silva) Irreducible unitary representations of some groups of real rank two, Non-Commutative Harmonic Analysis and Lie Groups, Lecture Notes in Mathematics 1243 (1987), Springer-Verlag, New York, pp. 15-36.
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  58. (with M. W. Baldoni-Silva) Vogan's algorithm for computing composition series, Non-Commutative Harmonic Analysis and Lie Groups, Lecture Notes in Mathematics 1243 (1987), Springer-Verlag, New York, pp. 37-72.
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  59. Lie Groups, Lie Algebras, and Cohomology, Princeton Mathematical Notes 34, Princeton University Press, Princeton, New Jersey, 1988.
    Access to the front matter and a list of corrections.

  60. (with M. W. Baldoni-Silva) Intertwining operators and unitary representations I, Journal of Functional Analysis 82 (1989), 151-236.
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  61. (with M. W. Baldoni-Silva) Intertwining operators and unitary representations II, Société Mathématique de France, Astérisque 171-172 (1989), 131-162.
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  62. (with M. W. Baldoni-Silva) A construction of unitary representations in parabolic rank two, Annali della Scuola Normale Superiore di Pisa 16 (1989), 579-601.
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  63. CRM Summer School Course on Representations of Real Reductive Groups, Publications CRM, Université de Montréal, Montréal, 1990.
    Access to the front matter.

  64. Imbedding discrete series in $L^2(G/H)$, in N. V. Pedersen (ed.), Harmonic Analysis on Lie Groups (Sandbjerg Estate, August 26-30, 1991), Copenhagen University Mathematics Institute, Report Series 1991, No. 3, Copenhagen, 1991, 27-29.
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  65. (with M. W. Baldoni-Silva) Intertwining operators into $L^2(G/H)$, Representation Theory of Lie Groups and Lie Algebras, Fuji-Kawaguchiko, Aug 31-Sep 3, 1990, T. Kawazoe, T. Oshima, and S. Sano (eds.), World Scientific, Singapore, 1992, pp. 95-119.
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  66. (with L. Barchini and R. Zierau) Intertwining operators into Dolbeault cohomology representations, Journal of Functional Analysis 107 (1992), 302-341.
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  67. Elliptic Curves, Princeton Mathematical Notes 40, Princeton University Press, Princeton, New Jersey, 1992.
    Access to the front matter and lists of corrections.  (This book grew out of notes of a course in India by Don Zagier in 1998.  To download a copy of the notes, click here.)

  68. Introduction to representations in analytic cohomology, The Penrose Transform and Analytic Cohomology in Representation Theory, M. Eastwood, J. Wolf, and R. Zierau (eds.), Contemporary Mathematics 154 (1993), American Mathematical Society, Providence, Rhode Island, pp. 1-19.
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  69. Local Langlands correspondence: the archimedean case, Motives, Proceedings of Symposia in Pure Mathematics 55 (1994), Part 2, American Mathematical Society, Providence, Rhode Island, pp. 393-410.
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  70. (with D. A. Vogan) Cohomological Induction and Unitary Representations, Princeton Mathematical Series 45, Princeton University Press, Princeton, New Jersey, 1995.
    Access to the front matter, the introduction, and a list of corrections.

  71. Group representations and harmonic analysis from Euler to Langlands, Part I, Notices of the American Mathematical Society 43 (1996), 410-415.
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  72. Group representations and harmonic analysis from Euler to Langlands, Part II, Notices of the American Mathematical Society 43 (1996), 537-549.
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  73. Lie Groups Beyond an Introduction, Progress in Mathematics 140, Birkhäuser, Boston, 1996. Reprinted with corrections, 2001.
    Access to the corrected pages appearing in the 2001 reprint.

  74. A quick proof of the classification of simple real Lie algebras, Proceedings of the American Mathematical Society 124 (1996), 3257-3259.
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  75. Exceptional unitary representations of semisimple Lie groups, Representation Theory 1 (1997), 1-24.
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  76. (editor with T. N. Bailey) Representation Theory and Automorphic Forms; An Instructional Conference at the International Centre for Mathematical Sciences, Edinburgh, 1996, Proceedings of Symposia in Pure Mathematics 61 (1997), American Mathematical Society, Providence, Rhode Island.
    Access to the front matter.

  77. Structure theory of semisimple Lie groups, Representation Theory and Automorphic Forms; An Instructional Conference at the International Centre for Mathematical Sciences, Edinburgh, 1996, Proceedings of Symposia in Pure Mathematics 61 (1997), American Mathematical Society, Providence, Rhode Island, pp. 1-27.
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  78. Introduction to the Langlands program, Representation Theory and Automorphic Forms; An Instructional Conference at the International Centre for Mathematical Sciences, Edinburgh, 1996, Proceedings of Symposia in Pure Mathematics 61 (1997), American Mathematical Society, Providence, Rhode Island, pp. 245-302.
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  79. Theoretical aspects of the trace formula for $GL(2)$, Representation Theory and Automorphic Forms; An Instructional Conference at the International Centre for Mathematical Sciences, Edinburgh, 1996, Proceedings of Symposia in Pure Mathematics 61 (1997), American Mathematical Society, Providence, Rhode Island, pp. 355-405.
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  80. (with J. D. Rogawski) Applications of the trace formula, Representation Theory and Automorphic Forms; An Instructional Conference at the International Centre for Mathematical Sciences, Edinburgh, 1996, Proceedings of Symposia in Pure Mathematics 61 (1997), American Mathematical Society, Providence, Rhode Island, pp. 413-431.
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  81. Survey of irreducible unitary representations of semisimple Lie groups, GROUP21: Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras, Proceedings of the XXI International Colloquium, vol. 1, World Scientific, Singapore, 1997, pp. 89-98.
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  82. André Weil: A prologue, Notices of the American Mathematical Society 46 (1999), 434-439.
    Abstract | Reprint in PDF.

  83. Anneli Lax's Research Mathematics, Notices of the American Mathematical Society 47 (2000), 768.
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  84. (with P. E. Trapa) Representations of semisimple Lie groups, Representation Theory of Lie Groups , J. Adams and D. Vogan (eds.), IAS/Park City Mathematics Series, vol. 8, American Mathematical Society, Providence, 2000, pp. 5-87.
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  85. Intertwining operators and small unitary representations, The Mathematical Legacy of Harish-Chandra; An AMS Special Session Honoring the Memory of Harish-Chandra, Baltimore, 1998, Proceedings of Symposia in Pure Mathematics 68 (2000), American Mathematical Society, Providence, Rhode Island, pp. 403-431.
    Abstract | Reprint in PDF.

  86. Nomination for David A. Vogan Jr. as President Elect of the American Mathematical Society, Notices of the American Mathematical Society 48 (2001), 853-854.
    Abstract | Reprint in PDF.

  87. Representation Theory of Semisimple Groups: An Overview Based on Examples, paperback reprint of the original 1986 hardback edition, Princeton Landmarks in Mathematics, Princeton University Press, 2001. ISBN: 0-691-09089-0.
    Access to the front matter and a list of corrections.

  88. Branching theorems for compact symmetric spaces, Representation Theory 5 (2001), 404-436.
    Abstract | Reprint in PDF.

  89. Lie Groups Beyond an Introduction, Second Edition, Progress in Mathematics, Vol. 140, Birkhäuser, Boston, 2002. ISBN: 0-8176-4259-5.
    Access to files of corrections, the front matter, and abstracts of chapters new or substantially changed from the first edition.

  90. The Gindikin-Karpelevic formula and intertwining operators, Lie Groups and Symmetric Spaces, In Memory of F. I. Karpelevich, American Mathematical Society Translations (2), 210 (2003), 145-159.
    Reprint in PDF.

  91. Geometric interpretations of two branching theorems of D.E. Littlewood, Journal of Algebra 270 (2003), 728-754.
    Abstract | Reprint in PDF.

  92. Analytic continuation of nonholomorphic discrete series for classical groups, Noncommutative Harmonic Analysis in Honor of Jacques Carmona, Progress in Mathematics, Vol. 220, Birkhäuser, Boston, 2004, pp. 253-289.
    ISBN: 0-8176-3207-7.
    Abstract | Reprint in PDF.

  93. Nilpotent orbits and some small unitary representations of indefinite orthogonal groups, Journal of Functional Analysis 209 (2004), 36-100.
    Abstract | Reprint in PDF.

  94. Salomon Bochner, August 20, 1899--May 2, 1982, Biographical Memoirs 85 (2004), 40-61.
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  95. ``Armand Borel (1923-2003),'' editor's note to article with eight authors, Notices of the American Mathematical Society 51 (2004), 498-524; republished in Asian Journal of Mathematics 8, No. 4 (2004), pp. xlvii-xlix.
    Reprint of Notices article in PDF | Reprint of editor's note from Asian Journal of Mathematics in PDF.

  96. ``Weil's letter to his sister,'' letter to the editor, Notices of the American Mathematical Society 52 (2005), 598-599.
    Reprint in PDF.

  97. Basic Real Analysis, Cornerstones, Birkhäuser, Boston, 2005. ISBN: 0-8176-3250-6.
    Access to the front matter and a list of corrections.

  98. Advanced Real Analysis, Cornerstones, Birkhäuser, Boston, 2005. ISBN: 0-8176-4382-6.
    Access to the front matter and a list of corrections.

  99. Basic Algebra, Cornerstones, Birkhäuser, Boston, 2006. ISBN: 0-8176-3248-4.
    Access to the front matter and a list of corrections.

  100. (with Henri Carayol) Limits of discrete series with infinitesimal character zero, Transactions of the American Mathematical Society 359 (2007), 5611-5651.
    Abstract | Reprint in PDF.

  101. Advanced Algebra, Cornerstones, Birkhäuser, Boston, 2007. ISBN: 0-8176-4522-5.
    Access to the front matter and a list of corrections.

  102. Prerequisites for the Langlands program, Automorphic Forms and the Langlands Program, Advanced Lectures in Mathematics 9 (2009), International Press, Somerville, Massachusetts, pp. 1-9.
    Abstract | Reprint in PDF.

  103. First steps with the Langlands program, Automorphic Forms and the Langlands Program, Advanced Lectures in Mathematics 9 (2009), International Press, Somerville, Massachusetts, pp. 10-20.
    Abstract | Reprint in PDF.

  104. Basic Real Analysis, digital second edition, published by the author, 2016; distributed by Project Euclid, 2018, with ISBN 978-1-4297-9999-7.
    Access to download 2016 version.

  105. Advanced Real Analysis, digital second edition, published by the author, 2016, corrected version, 2017; distributed by Project Euclid, 2018, with ISBN 978-1-4297-9991-1.
    Access to download 2017 version.

  106. Basic Algebra, digital second edition, published by the author, 2016; distributed by Project Euclid, 2018, with ISBN 978-1-4297-9998-0.
    Access to download 2016 version.  Access to a list of corrections.

  107. Advanced Algebra, digital second edition, published by the author, 2016; distributed by Project Euclid, 2018, with ISBN 978-1-4297-9992-8.
    Access to download 2016 version.

  108. Stokes's Theorem and Whitney Manifolds, original digital edition, published by the author, 2021; distributed by Project Euclid, 2021, with ISBN 978-1-4297-9988-1.
    Access to download 2021 version.

  109. Memorial tribute: Elias M. Stein (1931-2018), contributor to an article by Lillian B. Pierce with eighteen other contributors, Notices of the American Mathematical Society 68 (2021), 546-563.
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  110. Lie Groups Beyond an Introduction, digital second edition, published by the author, 2023; distributed by Project Euclid, 2023, with ISBN 979-8-9895-0420-6.
    Access to download 2023 version.



Book reviews
  1. Review of Lie Groups, Lie Algebras, and Their Representations by V. S. Varadarajan and Compact Lie Groups and Their Representations by D. P. Zhelobenko, Bulletin of the American Mathematical Society 81 (1975), 865-872.
    Reprint in PDF.

  2. Review of Unitary Representations of Reductive Lie Groups by D. A. Vogan, Bulletin of the American Mathematical Society (N.S.) 21 (1989), 380-384.
    Reprint in PDF.

  3. Review of Matrix Groups: An Introduction to Lie Group Theory by Andrew Baker and Lie Groups: An Introduction Through Linear Groups by Wulf Rossmann, American Mathematical Monthly 110 (2003), 446-455.
    Abstract | Reprint in PDF.

  4. Review of Love and Math: The Heart of Hidden Reality by Edward Frenkel, Notices of the American Mathematical Society 61 (2014), 1056-1060.
    Reprint in PDF.


Other writing
  1. (with P. Shaman) Certification of Algorithm 42, Invert, Communications of the Association for Computing Machinery 4(11) (1961), 498. Reprint in PDF.

  2. (with S. J. Garland) Algorithm 99, Evaluation of Jacobi symbol, Communications of the Association for Computing Machinery 5(6) (1962), 345-346. Reprint in PDF.

  3. Personal unofficial notes of a two-semester course Functional Analysis given by William Feller, Princeton University, Fall 1962 and Spring 1963. Scanned versions: PDF for Fall 1962, PDF for Spring 1963.

  4. (with A. Jackson) AMS in the Twentieth Century, Notices of the American Mathematical Society, 1999-2000. Reprint in PDF.

  5. Founding of the Episcopal Church, All Souls Episcopal Church, St. James, New York, 2007-08. Reprint in PDF.


Last modified: 6/21/2024