Charles F. Dunkl

Professor Emeritus of Mathematics
Department of Mathematics
P.O. Box 400137
University of Virginia
Charlottesville, VA 22904-4137

Phone: (voice) +1 434 924 4924 ; (fax) +1 434 982 3084
E-mail: cfd5z@virginia.edu

Background:

Membership in Professional Societies: Employment:

Books

Papers

  1. A simple norm inequality, American Math. Monthly 71 (1964), 53-54 (with K. S. Williams).
  2. Operators and harmonic analysis on the sphere, Trans. Amer. Math. Soc. 125 (1966), 250-263.
  3. Linear functionals on homogeneous polynomials, Canad. Math. Bull. 11 (1968), 465-468.
  4. Functions that operate in the Fourier algebra of a compact group, Proc. Amer. Math. Soc. 21 (1969), 540-544.
  5. Modules over commutative Banach algebras, Monatsh. Math. 74 (1970), 6-14.
  6. Translation in measure algebras and the correspondence to the Fourier transforms vanishing at infinity, Michigan Math. J.17 (1970), 311-319 (with D. Ramirez).
  7. L^p-multipliers on compact groups, Notices Amer. Math. Soc. 17 (1970), 955 (with D. Ramirez).
  8. Homomorphisms on groups and induced maps on certain algebras of measures, Trans. Amer. Math. Soc. 169 (1971), 475-485 (with D. Ramirez).
  9. C*-algebras generated by measures, Bull. Amer. Math. Soc. 77 (1971), 411-412 (with D. Ramirez).
  10. Multipliers on compact groups, Proc. Amer. Math. Soc. 28 (1971), 456-460 (with D. Ramirez).
  11. Sidon sets on compact groups, Monatsh. Math. 75 (1971), 111-117 (with D. Ramirez).
  12. Locally compact subgroups of the spectrum of the measure algebra, Semigroup Forum 3 (1971), 95-107 (with D. Ramirez).
  13. Locally compact subgroups of the spectrum of the measure algebra II, Semigroup Forum 3 (1971), 267-269 (with D. Ramirez).
  14. Helson sets in compact and locally compact groups, Michigan Math. J. 19 (1972), 65-69 (with D. Ramirez).
  15. C*-algebras generated by Fourier-Stieltjes transforms, Trans. Amer. Math. Soc. 164 (1972), 435-441 (with D. Ramirez).
  16. Weakly almost periodic functionals carried by hypercosets, Trans. Amer. Math. Soc. 164 (1972), 427-434 (with D. Ramirez).
  17. Singular integrals on ultraspherical series, Canad. J. Math. 24 (1972), 60-71.
  18. Bounded projections on Fourier-Stieltjes transforms, Proc. Amer. Math. Soc. 31 (1972), 122-126 (with D. Ramirez).
  19. Characterization of Sidon sets and Lambda-p sets on compact groups, Notices Amer. Math. Soc. 19 (1972), A436-A437 (with D. Ramirez).
  20. Subalgebras of the dual of the Fourier algebra of a compact group, Proc. Cambridge Philos. Soc. 71 (1972), 329-333 (with D. Ramirez).
  21. Fourier-Stieltjes transforms and weakly almost periodic functionals for compact groups, Pacific J. Math. 39 (1971), 637-639 (with D. Ramirez).
  22. Weakly sequentially complete function algebras, Notices Amer. Math. Soc. 19 (1972), A515-A516 (with D. Ramirez).
  23. Existence and nonuniqueness of invariant means on L(G), Proc. Amer. Math. Soc. 32 (1972), 525-530 (with D. Ramirez).
  24. L^p-convolution operators supported by subgroups, Proc. Amer. Math. Soc. 34 (1972), 475-478 (with D. Ramirez).
  25. Locally compact subgroups of the spectrum of the measure algebra III, Semigroup Forum 5 (1972), 65-76 (with D. Ramirez).
  26. Multipliers on modules over the Fourier algebras, Trans. Amer. Math. Soc .172 (1972), 357-364 (with D. Ramirez).
  27. The measure algebra of a locally compact hypergroup, Trans. Amer. Math. Soc. 179 (1973), 331-348.
  28. Structure hypergroups for measure algebras, Pacific J. Math. 47 (1973), 413-425.
  29. (a) Weakly almost periodic functionals on the Fourier algebra, Trans. Amer. Math. Soc. 185 (1973), 501-514 (with D. Ramirez). (b) Erratum to ``Weakly almost periodic functionals on the Fourier algebra,'' Trans. Amer. Math. Soc. 190 (1974), 427 (with D. Ramirez).
  30. L-infinity-representations of commutative semitopological semigroups, Semigroup Forum 7 (1974), 180-199 (with D. Ramirez).
  31. Sections induced from weakly sequentially complete spaces, Studia Math. 49 (1973), 95-97 (with D. Ramirez).
  32. Operators on the Fourier algebra with weakly compact extensions, Canad. J. Math. 26 (1974), 450-454 (with D. Ramirez).
  33. An expansion in ultraspherical polynomials with nonnegative coefficients, SIAM J. Math. Anal .5 (1974), 51-52.
  34. Krawtchouk polynomials and the symmetrization of hypergroups, SIAM J. Math. Anal. 5 (1974), 351-366 (with D. Ramirez).
  35. A family of countably compact P*-hypergroups, Trans. Amer. Math. Soc. 202 (1975), 339-356 (with D. Ramirez).
  36. Representations of commutative semitopological semigroups, Lecture Notes in Mathematics, Vol. 435. Springer-Verlag New York-Berlin (1975) (with D. Ramirez).
  37. Bounded derivations on commutative semigroups, Semigroup Forum 10 (1975), 229-237.
  38. A linear programming problem in harmonic analysis, Linear Algebra and its Applications 14 (1976), 107-116 (with D. Ramirez).
  39. A Krawtchouk polynomial addition theorem and wreath products of symmetric groups, Indiana Univ. Math. J. 25 (1976), 335-358.
  40. Spherical functions on compact groups and applications to special functions, Symposia Mathematica 22 (1977), 145-161.
  41. An addition theorem for Hahn polynomials: the spherical functions , SIAM J. Math. Anal. 9 (1978), 627-637.
  42. An addition theorem for some q-Hahn polynomials, Monatsh. Math. 85 (1977), 5-37.
  43. Discrete quadrature and bounds on t-designs, Michigan Math. J. 26 (1979), 81-102.
  44. Orthogonal functions on some permutation groups, Proc. of Symposia in Pure Math. 34 (1979), 129-147.
  45. A difference equation and Hahn polynomials in two variables, Pacific J. Math .92 (1981), 57-71.
  46. Orthogonal polynomials in two variables of q-Hahn and q -Jacobi type, SIAM J. Algebraic and Discrete Methods 1 (1980), 137-151.
  47. Cube group invariant spherical harmonics and Krawtchouk polynomials, Math. Z. 177 (1981), 561-577.
  48. The absorption distribution and the q-binomial theorem, Commun. Statist.-Theor. Meth. A10 (1981), 1915-1920.
  49. An addition theorem for Heisenberg harmonics, Conference on Harmonic Analysis in Honor of Antoni Zygmund. Wadsworth International (1982), 688-705.
  50. Orthogonal polynomials on the sphere with octahedral symmetry, Trans. Amer. Math. Soc. 282 (1984), 555-575.
  51. Orthogonal polynomials with symmetry of order three, Canad. J. Math. 36 (1984), 685-717.
  52. The Poisson kernel for Heisenberg polynomials on the disk, Math. Z. 187 (1984), 527-547.
  53. Orthogonal polynomials and a Dirichlet problem related to the Hilbert transform (CWI Report PM-R8406, 1984 Amsterdam), (Indag. Math.) Proc. Kon. Ned. Akad. van Wet.A88 (1985), 147-171.
  54. Boundary value problems for harmonic functions on the Heisenberg group, Canad. J. Math. 38 (1986), 478-512.
  55. Orthogonal polynomials on the hexagon, SIAM J. Appl. Math. 47 (1987), 343-351.
  56. Reflection groups and orthogonal polynomials on the sphere, Math. Z. 197 (1988), 33-60.
  57. Differential-difference operators associated to reflection groups , Trans. Amer. Math. Soc. 311 (1989), 167-183.
  58. Harmonic polynomials and peak sets on reflection groups, Geometriae Ded. 32 (1989), 157-171.
  59. Poisson and Cauchy kernels for orthogonal polynomials with dihedral symmetry, J. Math. Anal. Appl. 43 (1989), 459-470.
  60. Operators commuting with Coxeter group actions on polynomials, Invariant Theory and Tableaux, D. Stanton, ed., IMA vol. 19 , pp. 107-117, Springer-Verlag, New York 1990.
  61. Integral kernels with reflection group invariance, Canadian J. Math. 43 (1991), 1213-1227.
  62. Measures of Dirichlet type on regular polygons and their moments, J. Approx. Theory 69 (1992), 212-221.
  63. Computing hyperelliptic integrals for surface measure of ellipsoids, ACM Trans. Math.Software 20 (1994), 413-426 (with D. Ramirez).
  64. Algorithm 736: Hyperelliptic integrals and the surface measure of ellipsoids, ACM TOMS 20 (1994), 427-435 (with D. Ramirez).
  65. Hankel transforms associated to finite reflection groups, Contemp. Math. 138 (1992), 123-138.
  66. Differential-difference operators and monodromy representations of Hecke algebras, Pacific J. Math. 159 (1993), 271-298.
  67. Monodromy of hypergeometric functions for dihedral groups, Integral Transforms and Special Functions 1 (1993), 75-86.
  68. Singular polynomials for finite reflection groups, Trans. Amer. Math. Soc. 346 (1994), 237-256 (with M. de Jeu and E. Opdam).
  69. Intertwining operators associated to the group S3, Trans. Amer. Math. Soc. 347 (1995), 3347-3374.
  70. Integrals of polynomials associated with tableaux and the Garsia-Haiman conjecture, Math. Z . 228 (1998), 537-567 (with P. Hanlon).
  71. Intertwining operators and polynomials associated with the symmetric group, Monatsh. Math. 126 (1998), 181-209.
  72. Intertwining operators of type B_N, Algebraic Methods and q-Special Functions, J.F. van Diejen and L. Vinet, eds.; CRM Proc. & Lecture Notes, vol. 22, pp. 119-134; Amer. Math. Soc., 1999.
  73. Average c-efficiency, (with D. Ramirez) Interstat, Dec. 1997.
  74. Orthogonal polynomials of types A and B and related Calogero models, Commun. Math. Phys. 197 (1998), 451-487; q-alg/9710015.
  75. Computing with differential-difference operators, J. Symb. Comp. 28 (1999), 819-826.
  76. Planar harmonic polynomials of type B, J. Phys.A: Math. Gen. 32 (1999), 8095-8110.
  77. Computation of the generalized F distribution, Aust. N.Z. J. Stat. 43 (2001), 21-31 (with D. Ramirez).
  78. Polynomial eigenfunctions of the Calogero-Sutherland-Moser models with exchange terms, Calogero-Moser-Sutherland Models, J.F. van Diejen and L. Vinet, eds.; CRM Series in Mathematical Physics, pp. 37-51; Springer, New York-Berlin, 2000 (with T.H.Baker, P.J. Forrester).
  79. Generating functions associated with dihedral groups, Special Functions: Proceedings of the International Workshop, ( Hong Kong 21-25 June 1999) C. Dunkl, M. Ismail, R. Wong, eds., pp. 72-87; World Scientific Publishing, Singapore 2000.
  80. Orthogonal polynomials and reflection groups, Special Functions 2000, J. Bustoz et al. eds., pp. 111-128; Kluwer Acad. Publishers, Dordrecht, 2001.
  81. Zernike polynomials,  Supp. III, Encyclopaedia of Mathematics , M. Hazewinkel, ed., pp. 454-455; Kluwer Acad.Publishers, Dordrecht, 2002.
  82. Symmetric functions and B_N invariant spherical harmonics, J. Phys. A: Math. Gen. 35 (2002), 10391-10408.
  83. Dunkl operators for complex reflection groups, Proc. London Math. Soc. 86 (2003), 70-108 (with E. Opdam).
  84. Special functions and generating functions associated with reflection groups, J. Comp. Appl. Math. 153 (2003), 181-190.
  85. A Laguerre polynomial orthogonality and the hydrogen atom, Analysis and Appl. 1 (2003), 177-188.
  86. Singular polynomials for the symmetric group and Krawtchouk polynomials, Development of the Mathematical Ideas of Mykhailo Kravchuk, N. Virchenko et al, eds., pp. 363-373;  Nat.Tech. Univ. Ukraine (KPI), Kyiv-New York, 2004.
  87. Singular polynomials for the symmetric groups, Int. Math. Res. Not. 2004 #67, 3607-3635.
  88. Singular polynomials and modules for the symmetric groups,  Int. Math. Res. Not. 2005 #39, 2409-2436.
  89. Nonsymmetric Jack polynomials and Calogero-Moser models, Group Theoretical Methods in Physics, (Cocoyoc, Mexico, 2-6 August 2004) G. S. Pogosyan, L. E.Vincent, K. B. Wolf, eds., pp. 45-51; IoP Conference Series No. 185, Bristol-Philadelphia
  90. Hook-lengths and pairs of compositions, J. Comp. Appl. Math. 199 (2007), 39-47.
  91. Polynomials associated with dihedral groups, SIGMA 3 (2007) 52, 19pp., arXiv:math.CA/072107.
  92. An intertwining operator for the group B2, Glasgow Math. J. 49 (2007), 291-319.
  93. Some orthogonal polynomials in four variables, SIGMA 4 (2008) 82, 9pp. arXiv:0812.0063.
  94. Transforms, polynomials and integral models associated with reflection groups, Infinite Dimensional Harmonic Analysis IV, (University of Tokyo 10-14 Sept. 2007)  J. Hilgert et al. eds., pp. 47-62, World Scientific Publishing, Singapore, 2009
  95. Reflection groups in analysis and applications, Japanese J. Math. 3 (2008), 215-246.
  96. Volume of the set of unistochastic matrices of order 3 and the mean Jarlskog invariant, J. Math. Physics 50 (2009), 123521 (25 pp.) (with K. Życzkowski)
  97. Symmetric and antisymmetric vector-valued Jack polynomials, Sém. Lothar. Combin. B64a (2010), 31 pp.
  98. Generalized Jack polynomials and the representation theory of rational Cherednik algebras, Selecta Math. (N.S.) 16 (2010), 791-818 (with S. Griffeth)
  99. Numerical shadows: Measures and densities on the numerical range, Linear Algebra and its Applications, 434 (2011), 2042-2080; DOI: 10.1016/j.laa.2010.12.003 (with P. Gawron, J. Holbrook, Z. Puchała, K. Życzkowski)
  100. Vector-Valued Jack Polynomials from Scratch, SIGMA 7 (2011) 26, 48 pp. (with J-G. Luque)
  101. Numerical shadow and geometry of quantum states, J. Phys. A: Math. Theor. 44 (2011), 335301 (19pp) (with P. Gawron, J. Holbrook, J. Miszczak, Z. Puchała, K. Życzkowski)
  102. Vector valued Macdonald polynomials, Sém. Lothar. Combin. B66b (2011), 68 pp. (with J.-G. Luque)
  103. Restricted numerical shadow and the geometry of quantum entanglement, J. Phys. A: Math. Theor. 45 (2012), 415309 (28 pp.) (with Z. Puchała, J. Miszczak, P. Gawron, J. Holbrook, K. Życzkowski)
  104. Vector-valued polynomials and a matrix weight function with B2-action, SIGMA 9 (2013), 007, 23 pages, arxiv:1210.1177
  105. Vector-valued polynomials and a matrix weight function with B2-action, II, SIGMA 9 (2013), 043, 11 pages
  106. Some Rarita-Schwinger type operators, Comput. Methods Funct. Theory, 13 (2013), 397-424 (with J. Li, J. Ryan, P. Van Lancker)
  107. Vector polynomials and a matrix weight associated to dihedral groups, SIGMA 10 (2014), 044, 23 pages
  108. Generalized two-qubit whole and half Hilbert-Schmidt separability probabilities, J. Geometry and Physics 90 (2015), 42-54 (with P. Slater)
  109. Real numerical shadows and generalized B-splines, Linear Algebra and its Applications 479 (2015), 12-51, DOI: 10/1016/j.laa.2015.03.029 (with P. Gawron, .Ł. Pawela, Z. Puchała, K. Życzkowski)
  110. Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States, Advances in Mathematical Physics 2015, article ID 62153, 9 pages, DOI:10.1155/2015/621353 (with P. Slater)
  111. Clustering properties of rectangular Macdonald polynomials, Ann. Inst. Henri Poincaré Comb. Phys. Interact. 2 (2015), 263-307, DOI:10.4171/AIHPD/19 (with J.-G. Luque)
  112. Separability probability formulas and their proofs for generalized two-qubit X-Matrices endowed with Hilbert–Schmidt and induced measures, Random Matrices: Theory Appl. 4 (2015), 1550018, DOI: 10.1142/S2010326315500185, (with P. Slater)
  113. Orthogonality measure on the torus for vector-valued Jack polynomials, SIGMA 12 (2016), 033, 27 pages
  114. Planar harmonic and monogenic polynomials of type A, Symmetry 8 (2016), 108, DOI:10.3390/sym8100108*
  115. Vector-valued Jack polynomials and wavefunctions on the torus, J. Phys. A: Math. Theor. 50 (2017) 245201 (21pp) https://doi.org/10.1088/1751-8121/aa6fb9
  116. A linear system of differential equations related to vector-valued Jack polynomials on the torus, SIGMA 13 (2017), 040, 41 pages
Updated by C. Dunkl,  7 June 2017