An Introduction to Dunkl Theory and Its Analytic Aspects (Q4644991)

scientific article; zbMATH DE number 6999156

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English	An Introduction to Dunkl Theory and Its Analytic Aspects	scientific article; zbMATH DE number 6999156

Statements

instance of

scholarly article

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title

An Introduction to Dunkl Theory and Its Analytic Aspects (English)

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author

Jean-Philippe Anker

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published in

Trends in Mathematics

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publication date

9 January 2019

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full work available at URL

https://arxiv.org/abs/1611.08213

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zbMATH Keywords

Dunkl theory

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special functions associated with root systems

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spherical Fourier analysis

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MaRDI profile type

Publication

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cites work

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Riesz transforms for Dunkl transform

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Three results in Dunkl analysis

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Opdam's hypergeometric functions: product formula and convolution structure in dimension 1

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The Hardy space $H^1$ in the rational Dunkl setting

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Laguerre semigroup and Dunkl operators

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Explicit formulas for the Dunkl dihedral kernel and the $(\kappa,a)$-generalized Fourier kernel

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Estimates for functions of the Laplace operator on homogeneous trees

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Paley–Wiener theorems for the Dunkl transform

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Asymptotic analysis for the Dunkl kernel

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Dunkl kernel associated with dihedral groups

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Differential-Difference Operators Associated to Reflection Groups

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Intertwining Operators Associated to the Group S 3

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AN INTERTWINING OPERATOR FOR THE GROUP B2

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Q2703812

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Riesz transforms characterizations of Hardy spaces $H^1$ for the rational Dunkl setting and multidimensional Bessel operators

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Liouville's property and Poisson's equation for the generalized Dunkl Laplacian.

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A new mean value property for harmonic functions relative to the Dunkl-Laplacian operator and applications

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Newtonian potentials and subharmonic functions associated to root systems

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Support properties of the intertwining and the mean value operators in Dunkl theory

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Macdonald formula for spherical functions on affine buildings

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Some applications of hypergeometric shift operators

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Harmonic analysis for certain representations of graded Hecke algebras

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POSITIVITY OF THE TRANSMUTATION OPERATORS AND ABSOLUTE CONTINUITY OF THEIR REPRESENTING MEASURES FOR A ROOT SYSTEM ON $\mathbb{R}^d$

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Product formulas for a two-parameter family of Heckman-Opdam hypergeometric functions of type BC

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describes a project that uses

Digital Library of Mathematical Functions

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Identifiers

zbMATH Open document ID

1404.33014

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DOI

10.1007/978-3-319-52842-7_1

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:4644991