2001, Encyclopedia of mathematics and its applications, ISBN 0521800439, Volume 81., xv, 390

This is the first modern book on orthogonal polynomials of several variables, which are interesting both as objects of study and as tools used in multivariate...

Functions of several real variables | Orthogonal polynomials

Functions of several real variables | Orthogonal polynomials

Book

1975, Lecture notes in mathematics, ISBN 9780387071329, Volume 435., vi, 181

Book

Integral Transforms and Special Functions, ISSN 1065-2469, 02/2015, Volume 26, Issue 2, pp. 88 - 89

Integral Transforms and Special Functions Proceedings of OPSFA12, 2013

Journal Article

Proceedings of the London Mathematical Society, ISSN 0024-6115, 1/2003, Volume 86, Issue 1, pp. 70 - 108

Dunkl operators for complex reflection groups are defined in this paper. These commuting operators give rise to a parameterized family of deformations of the...

complex reflection group | Dunkl operator | rational Cherednik algebra | POLYNOMIALS | MATHEMATICS | HECKE ALGEBRAS | BRAID-GROUPS

complex reflection group | Dunkl operator | rational Cherednik algebra | POLYNOMIALS | MATHEMATICS | HECKE ALGEBRAS | BRAID-GROUPS

Journal Article

11/2006, ISBN 3540071326, 188

eBook

Journal of Symbolic Computation, ISSN 0747-7171, 12/1999, Volume 28, Issue 6, pp. 819 - 826

Computer algebra can be used to prove identities in the algebra of operators on polynomials which is generated by multiplication by coordinate functions, and...

MATHEMATICS, APPLIED | REFLECTION | ORTHOGONAL POLYNOMIALS | COMPUTER SCIENCE, THEORY & METHODS | Algebra

MATHEMATICS, APPLIED | REFLECTION | ORTHOGONAL POLYNOMIALS | COMPUTER SCIENCE, THEORY & METHODS | Algebra

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 1994, Volume 346, Issue 1, pp. 237 - 256

Journal Article

Indagationes Mathematicae, ISSN 0019-3577, 1985, Volume 47, Issue 2, pp. 147 - 171

An operator closely related to the Hilbert transform on the circle is shown to be unitarily equivalent to a shift realized on a basis of Pollaczek polynomials,...

Journal Article

Japanese Journal of Mathematics, ISSN 0289-2316, 12/2008, Volume 3, Issue 2, pp. 215 - 246

This is an overview of the use of reflection groups in analysis, applications in algebra, mathematical physics, and probability.

Dunkl transform | non-symmetric Jack polynomials | 82 (secondary) | Mathematics, general | 42 (primary) | Mathematics | Dunkl operators | Calogero–Sutherland models | History of Mathematics | Calogero-Sutherland models | Non-symmetric Jack polynomials | MATHEMATICS | ADDITION THEOREM | REPRESENTATION | ORTHOGONAL POLYNOMIALS | SINGULAR POLYNOMIALS | FORMULA | KERNELS

Dunkl transform | non-symmetric Jack polynomials | 82 (secondary) | Mathematics, general | 42 (primary) | Mathematics | Dunkl operators | Calogero–Sutherland models | History of Mathematics | Calogero-Sutherland models | Non-symmetric Jack polynomials | MATHEMATICS | ADDITION THEOREM | REPRESENTATION | ORTHOGONAL POLYNOMIALS | SINGULAR POLYNOMIALS | FORMULA | KERNELS

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 03/2016, Volume 12

For each irreducible module of the symmetric group on [...] objects there is a set of parametrized nonsymmetric Jack polynomials in [...] variables taking...

Fourier-stieltjes coefficients | Matrix-valued measure | Nonsymmetric Jack polynomials | Symmetric group modules

Fourier-stieltjes coefficients | Matrix-valued measure | Nonsymmetric Jack polynomials | Symmetric group modules

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2008, Volume 4, p. 082

The symmetric group on 4 letters has the reflection group D-3 as an isomorphic image. This fact follows from the coincidence of the root systems A(3) and D-3....

Nonsymmetric jack polynomials | JACK POLYNOMIALS | PHYSICS, MATHEMATICAL | nonsymmetric Jack polynomials | BINOMIAL FORMULA

Nonsymmetric jack polynomials | JACK POLYNOMIALS | PHYSICS, MATHEMATICAL | nonsymmetric Jack polynomials | BINOMIAL FORMULA

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 03/1988, Volume 197, Issue 1, pp. 33 - 60

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 04/2003, Volume 153, Issue 1-2, pp. 181 - 190

This is a survey paper concerning multi-variable special functions associated with finite reflection groups. The key tool is the algebra of...

Icosahedron | Orthogonal polynomials | Dunkl operators | POLYNOMIALS | MATHEMATICS, APPLIED | OPERATORS | icosahedron | orthogonal polynomials | Algebra

Icosahedron | Orthogonal polynomials | Dunkl operators | POLYNOMIALS | MATHEMATICS, APPLIED | OPERATORS | icosahedron | orthogonal polynomials | Algebra

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2018, Volume 14

There is a space of vector-valued nonsymmetric Jack polynomials associated with any irreducible representation of a symmetric group. Singular polynomials for...

Standard modules | Young tableaux | Nonsymmetric jack polynomials | PHYSICS, MATHEMATICAL | nonsymmetric Jack polynomials | standard modules | Polynomials | Mathematics - Representation Theory

Standard modules | Young tableaux | Nonsymmetric jack polynomials | PHYSICS, MATHEMATICAL | nonsymmetric Jack polynomials | standard modules | Polynomials | Mathematics - Representation Theory

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 10/2012, Volume 45, Issue 41, pp. 415309 - 28

The restricted numerical range W-R(A) of an operator A acting on a D-dimensional Hilbert space is defined as a set of all possible expectation values of this...

STATES | RANGES | UNITARY | PHYSICS, MULTIDISCIPLINARY | INFORMATION | MATRICES | PHYSICS, MATHEMATICAL | Shadows | Operators | Planes | Dynamics | Quantum mechanics | Hilbert space | Entanglement | Entangled states | Invariants

STATES | RANGES | UNITARY | PHYSICS, MULTIDISCIPLINARY | INFORMATION | MATRICES | PHYSICS, MATHEMATICAL | Shadows | Operators | Planes | Dynamics | Quantum mechanics | Hilbert space | Entanglement | Entangled states | Invariants

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2011, Volume 434, Issue 9, pp. 2042 - 2080

For any operator acting on an -dimensional Hilbert space we introduce its , which is a probability measure on the complex plane supported by the numerical...

Non-normal matrices | Numerical range | Numerical shadow | Probability measures | Higher-rank numerical range | MATHEMATICS | MATHEMATICS, APPLIED

Non-normal matrices | Numerical range | Numerical shadow | Probability measures | Higher-rank numerical range | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2013, Volume 9, p. 043

This is a sequel to [SIGMA 9 (2013), 007, 23 pages], in which there is a construction of a 2×2 positive-definite matrix function K(x) on R2. The entries of...

Matrix gaussian weight function | matrix Gaussian weight function

Matrix gaussian weight function | matrix Gaussian weight function

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 04/2014, Volume 10

The space of polynomials in two real variables with values in a 2-dimensional irreducible module of a dihedral group is studied as a standard module for...

Standard module | Gaussian weight | Mathematics - Classical Analysis and ODEs

Standard module | Gaussian weight | Mathematics - Classical Analysis and ODEs

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2013, Volume 9, p. 007

The structure of orthogonal polynomials on [...] with the weight function [...] is based on the Dunkl operators of type [...]. This refers to the full...

Harmonic polynomials | Matrix Gaussian weight function | matrix Gaussian weight function | harmonic polynomials

Harmonic polynomials | Matrix Gaussian weight function | matrix Gaussian weight function | harmonic polynomials

Journal Article

Mineralogical Magazine, ISSN 0026-461X, 2018, Volume 82, Issue 3, pp. 751 - 778

The historic Waterberg platinum deposit, similar to 15 km WNW of Mookgophong (formerly Naboomspruit), Limpopo Province, South Africa, is a rare fault-bound...

cathodoluminescence | fluid inclusions | hematite geochronology | Waterberg platinum deposit | quartz-hematite-PGE mineralization | oxygen isotopes | trace elements in quartz | GOLD | GENESIS | SOLUBILITY | TITANIQ | HEMATITE | TEMPERATURE | MINERALIZATION | MINAS-GERAIS | SILICA | MINERALOGY | INSIGHTS | Mineralogy | Carbon dioxide | Geochemistry | Minerals | Brines | Platinum | Mineralization | Stable isotopes | Kaolinite | Isotopes | Age | Cooling | Geology | Fluid | Museums | Acidity | Earth science | Sodium chloride | Quartz | Ablation | Calcium chloride | Salinity | Studies | Microscopy | Upwelling | Trace elements | Iron oxides | Mass spectrometry

cathodoluminescence | fluid inclusions | hematite geochronology | Waterberg platinum deposit | quartz-hematite-PGE mineralization | oxygen isotopes | trace elements in quartz | GOLD | GENESIS | SOLUBILITY | TITANIQ | HEMATITE | TEMPERATURE | MINERALIZATION | MINAS-GERAIS | SILICA | MINERALOGY | INSIGHTS | Mineralogy | Carbon dioxide | Geochemistry | Minerals | Brines | Platinum | Mineralization | Stable isotopes | Kaolinite | Isotopes | Age | Cooling | Geology | Fluid | Museums | Acidity | Earth science | Sodium chloride | Quartz | Ablation | Calcium chloride | Salinity | Studies | Microscopy | Upwelling | Trace elements | Iron oxides | Mass spectrometry

Journal Article

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