**Phone:** (voice) +1 434 924 4924 ; (fax) +1 434 982 3084

**E-mail:** cfd5z@virginia.edu

**Background:**

*Place of Birth*: Vienna, Austria*Nationality:*U.S.A*.**Highest Degree:*Ph.D. 1965

- Fellow of the Institute of Physics (IOP, London)

- Society for Industrial and Applied Mathematics (SIAM)
- Founder 1990, Chair 1990-1998, Secretary 1999-2001, SIAM Activity Group on Orthogonal Polynomials and Special Functions

- Professor Emeritus (2005-present),
University of Virginia

*Professor*(1980-2005), University of Virginia*Member*(March 2001- July 2001), Isaac Newton Institute for Mathematical Sciences, Cambridge

*Visiting Associate Professor*(1977-1978), Georgia Institute of Technology*Associate Professor*(1970-1980), University of Virginia*Assistant Professor*(1967-1970), University of Virginia*Instructor*(1965-1967), Princeton University

*Topics in Harmonic Analysis,*(with D. Ramirez) Appleton-Century-Crofts, New York: (Irvington Press) , 1971.*Special Functions: Proceedings of the International Workshop*; edited by C. D., M. Ismail, R. Wong; World Scientific Publishers, Singapore, 2000. ISBN 981-02-4393-6*Orthogonal Polynomials of Several Variables*; (with Y. Xu) Encyclopedia of Mathematics and its Applications (81), Cambridge University Press, Cambridge, 2001. ISBN 0-521-80043-9*Orthogonal Polynomials of Several Variables*; Second edition, (with Y. Xu) Encyclopedia of Mathematics and its Applications (155), Cambridge University Press, Cambridge, 2014, ISBN 978-1-107-07189-6

- A simple norm inequality,
*American Math. Monthly***71**(1964), 53-54 (with K. S. Williams). - Operators and harmonic analysis on the sphere,
*Trans. Amer. Math. Soc*.**125**(1966), 250-263. - Linear functionals on homogeneous polynomials,
*Canad. Math. Bull.***11**(1968), 465-468. - Functions that operate in the Fourier algebra of a compact
group,
*Proc. Amer. Math. Soc*.**21**(1969), 540-544. - Modules over commutative Banach algebras,
*Monatsh. Math*.**74**(1970), 6-14. - Translation in measure algebras and the correspondence to the
Fourier transforms vanishing at infinity,
*Michigan Math. J.***17**(1970), 311-319 (with D. Ramirez). *L^p*-multipliers on compact groups,*Notices Amer. Math. Soc.***17**(1970), 955 (with D. Ramirez).- Homomorphisms on groups and induced maps on certain algebras
of measures,
*Trans. Amer. Math. Soc.***169**(1971), 475-485 (with D. Ramirez). *C**-algebras generated by measures,*Bull. Amer. Math. Soc.***77**(1971), 411-412 (with D. Ramirez).- Multipliers on compact groups,
*Proc. Amer. Math. Soc.***28**(1971), 456-460 (with D. Ramirez). - Sidon sets on compact groups,
*Monatsh. Math.***75**(1971), 111-117 (with D. Ramirez). - Locally compact subgroups of the spectrum of the measure
algebra,
*Semigroup Forum***3**(1971), 95-107 (with D. Ramirez). - Locally compact subgroups of the spectrum of the measure
algebra II,
*Semigroup Forum***3**(1971), 267-269 (with D. Ramirez). - Helson sets in compact and locally compact groups,
*Michigan Math. J.***19**(1972), 65-69 (with D. Ramirez). *C**-algebras generated by Fourier-Stieltjes transforms,*Trans. Amer. Math. Soc*.**164**(1972), 435-441 (with D. Ramirez).- Weakly almost periodic functionals carried by hypercosets,
*Trans. Amer. Math. Soc.***164**(1972), 427-434 (with D. Ramirez). - Singular integrals on ultraspherical series,
*Canad. J. Math.***24**(1972), 60-71. - Bounded projections on Fourier-Stieltjes transforms,
*Proc. Amer. Math. Soc.***31**(1972), 122-126 (with D. Ramirez). - Characterization of Sidon sets and Lambda-
*p*sets on compact groups,*Notices Amer. Math. Soc.***19**(1972), A436-A437 (with D. Ramirez). - Subalgebras of the dual of the Fourier algebra of a compact
group,
*Proc. Cambridge Philos. Soc.***71**(1972), 329-333 (with D. Ramirez). - Fourier-Stieltjes transforms and weakly almost periodic
functionals for compact groups,
*Pacific J. Math*.**39**(1971), 637-639 (with D. Ramirez). - Weakly sequentially complete function algebras,
*Notices Amer. Math. Soc.***19**(1972), A515-A516 (with D. Ramirez). - Existence and nonuniqueness of invariant means on
*L(G)*,*Proc. Amer. Math. Soc.***32**(1972), 525-530 (with D. Ramirez). *L^p*-convolution operators supported by subgroups,*Proc. Amer. Math. Soc.***34**(1972), 475-478 (with D. Ramirez).- Locally compact subgroups of the spectrum of the measure
algebra III,
*Semigroup Forum***5**(1972), 65-76 (with D. Ramirez). - Multipliers on modules over the Fourier algebras,
*Trans. Amer. Math. Soc .***172**(1972), 357-364 (with D. Ramirez). - The measure algebra of a locally compact hypergroup,
*Trans. Amer. Math. Soc.***179**(1973), 331-348. - Structure hypergroups for measure algebras,
*Pacific J. Math.***47**(1973), 413-425. - (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). *L*-infinity-representations of commutative semitopological semigroups,*Semigroup Forum***7**(1974), 180-199 (with D. Ramirez).- Sections induced from weakly sequentially complete spaces,
*Studia Math.***49**(1973), 95-97 (with D. Ramirez). - Operators on the Fourier algebra with weakly compact
extensions,
*Canad. J. Math.***26**(1974), 450-454 (with D. Ramirez). - An expansion in ultraspherical polynomials with nonnegative
coefficients,
*SIAM J. Math. Anal .***5**(1974), 51-52. - Krawtchouk polynomials and the symmetrization of hypergroups,
*SIAM J. Math. Anal.***5**(1974), 351-366 (with D. Ramirez). - A family of countably compact
*P**-hypergroups,*Trans. Amer. Math. Soc.***202**(1975), 339-356 (with D. Ramirez). - Representations of commutative semitopological semigroups,
*Lecture Notes in Mathematics*, Vol.**435**. Springer-Verlag New York-Berlin (1975) (with D. Ramirez). - Bounded derivations on commutative semigroups,
*Semigroup Forum***10**(1975), 229-237. - A linear programming problem in harmonic analysis,
*Linear Algebra and its Applications***14**(1976), 107-116 (with D. Ramirez). - A Krawtchouk polynomial addition theorem and wreath products
of symmetric groups,
*Indiana Univ. Math. J.***25**(1976), 335-358. - Spherical functions on compact groups and applications to
special functions,
*Symposia Mathematica***22**(1977), 145-161. - An addition theorem for Hahn polynomials: the spherical
functions
*, SIAM J. Math. Anal.***9**(1978), 627-637. - An addition theorem for some
*q*-Hahn polynomials,*Monatsh. Math.***85**(1977), 5-37. - Discrete quadrature and bounds on
*t*-designs,*Michigan Math. J.***26**(1979), 81-102. - Orthogonal functions on some permutation groups,
*Proc. of Symposia in Pure Math.***34**(1979), 129-147. - A difference equation and Hahn polynomials in two variables,
*Pacific J. Math .***92**(1981), 57-71. - Orthogonal polynomials in two variables of
*q*-Hahn and*q*-Jacobi type,*SIAM J. Algebraic and Discrete Methods***1**(1980), 137-151. - Cube group invariant spherical harmonics and Krawtchouk
polynomials,
*Math. Z.***177**(1981), 561-577. - The absorption distribution and the
*q-*binomial theorem,*Commun. Statist.-Theor. Meth.***A10**(1981), 1915-1920. - An addition theorem for Heisenberg harmonics,
*Conference on Harmonic Analysis in Honor of Antoni Zygmund*. Wadsworth International (1982), 688-705. - Orthogonal polynomials on the sphere with octahedral
symmetry,
*Trans. Amer. Math. Soc*.**282**(1984), 555-575. - Orthogonal polynomials with symmetry of order three,
*Canad. J. Math.***36**(1984), 685-717. - The Poisson kernel for Heisenberg polynomials on the disk,
*Math. Z*.**187**(1984), 527-547. - 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. - Boundary value problems for harmonic functions on the
Heisenberg group,
*Canad. J. Math.***38**(1986), 478-512. - Orthogonal polynomials on the hexagon,
*SIAM J. Appl. Math.***47**(1987), 343-351. - Reflection groups and orthogonal polynomials on the sphere,
*Math. Z*.**197**(1988), 33-60. __Differential-difference operators associated to reflection groups__,*Trans. Amer. Math. Soc*.**311**(1989), 167-183.- Harmonic polynomials and peak sets on reflection groups,
*Geometriae Ded*.**32**(1989), 157-171. - Poisson and Cauchy kernels for orthogonal polynomials with
dihedral symmetry,
*J. Math. Anal. Appl.***43**(1989), 459-470. - 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. - Integral kernels
with reflection group invariance,
*Canadian J. Math.***43**(1991), 1213-1227. - Measures of Dirichlet type on regular polygons and their
moments,
*J. Approx. Theory***69**(1992), 212-221. - Computing hyperelliptic integrals for surface measure of
ellipsoids,
*ACM Trans. Math.Software***20**(1994), 413-426 (with D. Ramirez). - Algorithm 736: Hyperelliptic integrals and the surface
measure of ellipsoids,
*ACM TOMS***20**(1994), 427-435 (with D. Ramirez). - Hankel transforms
associated to finite reflection groups,
*Contemp. Math*.**138**(1992), 123-138. - Differential-difference operators and monodromy
representations of Hecke algebras,
*Pacific J. Math.***159**(1993), 271-298. - Monodromy of hypergeometric functions for dihedral groups,
*Integral Transforms and Special Functions***1**(1993), 75-86. - Singular polynomials for finite reflection groups,
*Trans. Amer. Math. Soc.***346**(1994), 237-256 (with M. de Jeu and E. Opdam). - Intertwining operators associated to the group
*S3*,*Trans. Amer. Math. Soc.***347**(1995), 3347-3374. - Integrals of polynomials associated with tableaux and the
Garsia-Haiman conjecture,
*Math. Z .***228**(1998), 537-567 (with P. Hanlon). - Intertwining operators and polynomials associated with the
symmetric group,
*Monatsh. Math.***126**(1998), 181-209. - 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. - Average
*c*-efficiency, (with D. Ramirez)*Interstat*, Dec. 1997. - Orthogonal polynomials of types
*A*and*B*and related Calogero models,*Commun. Math. Phys.***197**(1998), 451-487; q-alg/9710015. - Computing with differential-difference operators,
*J. Symb. Comp.***28**(1999), 819-826. - Planar harmonic polynomials of type
*B*,*J. Phys.A: Math. Gen.***32**(1999), 8095-8110. - Computation of the generalized
*F*distribution,*Aust. N.Z. J. Stat.***43**(2001), 21-31 (with D. Ramirez). - 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). - 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. - Orthogonal polynomials and reflection groups,
*Special Functions 2000*, J. Bustoz et al. eds., pp. 111-128; Kluwer Acad. Publishers, Dordrecht, 2001. - Zernike polynomials,
*Supp. III, Encyclopaedia of Mathematics*, M. Hazewinkel, ed., pp. 454-455; Kluwer Acad.Publishers, Dordrecht, 2002. - Symmetric functions and
*B_N*invariant spherical harmonics,*J. Phys. A: Math. Gen.***35**(2002), 10391-10408. - Dunkl operators for
complex reflection groups,
*Proc. London Math. Soc.***86**(2003), 70-108 (with E. Opdam). - Special functions and generating functions associated with
reflection groups,
*J. Comp. Appl. Math.***153**(2003), 181-190. - A Laguerre polynomial orthogonality and the hydrogen atom,
*Analysis and Appl.***1**(2003), 177-188. - 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.

- Singular polynomials for the symmetric groups, Int. Math. Res. Not. 2004 #67, 3607-3635.
- Singular polynomials and modules for the symmetric groups, Int. Math. Res. Not. 2005 #39, 2409-2436.
- 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

- Hook-lengths and pairs of compositions, J. Comp. Appl. Math. 199 (2007), 39-47.
- Polynomials associated with dihedral groups, SIGMA 3 (2007) 52, 19pp., arXiv:math.CA/072107.
- An intertwining operator for the group B2, Glasgow Math. J. 49 (2007), 291-319.
- Some orthogonal polynomials in four variables, SIGMA 4 (2008) 82, 9pp. arXiv:0812.0063.
- 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

- Reflection groups in analysis and applications, Japanese J. Math. 3 (2008), 215-246.
- 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)
- Symmetric and antisymmetric vector-valued Jack polynomials, Sém. Lothar. Combin. B64a (2010), 31 pp.
- Generalized Jack polynomials and the representation theory of rational Cherednik algebras, Selecta Math. (N.S.) 16 (2010), 791-818 (with S. Griffeth)
- 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)
- Vector-Valued Jack Polynomials from Scratch, SIGMA 7 (2011) 26, 48 pp. (with J-G. Luque)
- 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) - Vector valued Macdonald polynomials, Sém. Lothar. Combin. B66b (2011), 68 pp. (with J.-G. Luque)
- 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) - Vector-valued
polynomials and a matrix weight function with B2-action,
*SIGMA***9**(2013), 007, 23 pages, arxiv:1210.1177 - Vector-valued
polynomials and a matrix weight function with B2-action, II,
*SIGMA***9**(2013), 043, 11 pages - Some
Rarita-Schwinger type operators,
*Comput. Methods Funct. Theory,***13**(2013), 397-424 (with J. Li, J. Ryan, P. Van Lancker) - Vector
polynomials and a matrix weight associated to dihedral
groups,
*SIGMA***10**(2014), 044, 23 pages - Generalized two-qubit whole and half Hilbert-Schmidt
separability probabilities,
*J. Geometry and Physics***90**(2015), 42-54 (with P. Slater) - 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) - 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) - 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) - 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) - Orthogonality measure on the torus for vector-valued Jack
polynomials,
*SIGMA***12**(2016), 033, 27 pages - Planar harmonic and monogenic polynomials of type
*A*,*Symmetry***8**(2016), 108, DOI:10.3390/sym8100108* - 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 - A linear system of differential equations related to
vector-valued Jack polynomials on the torus,
*SIGMA***13**(2017), 040, 41 pages - A family of Crouzeix-Raviart finite elements in
*3D*,*Analysis and Appl***16**(2018), 649-691,*.*https://doi.org/10.1142/S0219530518500070 - The smallest singular values and vector-valued Jack
polynomials,
*SIGMA***14**(2018), 115, 20 pages, doi.org/10.3842/SIGMA.2018.115 - Factorizations of symmetric Macdonald polynomials,
*Symmetry***2018**10(11), 541, doi.org/10.3390/sym10110541 (with L. Colmenarejo and J.-G. Luque) - A Positive-Definite Inner Product for Vector-Valued Macdonald
Polynomial, Sém.
Lothar. Combin
**B80a**(2019), 26pp.