On the kernel of the -Generalized fourier transform

DOI10.1017/fms.2023.69zbMath1528.42016arXiv2210.15730MaRDI QIDQ6135387

Sergey Yu. Tikhonov, Dmitry Gorbachev, Valeriĭ I. Ivanov

Publication date: 25 August 2023

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2210.15730

zbMATH Keywords

kernelSchwartz spaceDunkl transform\((k,\alpha)\)-generalized Fourier transform

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal polynomials and functions associated with root systems (33C52)

Related Items

Nondeformed generalized Dunkl transform on the line ⋮ Unnamed Item

Cites Work

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• Explicit formulas for the Dunkl dihedral kernel and the \((\kappa,a)\)-generalized Fourier kernel
• Generalized Bessel functions of dihedral-type: expression as a series of confluent Horn functions and Laplace-type integral representation
• The Dunkl transform
• Positivity of Dunkl's intertwining operator
• The Dunkl kernel and intertwining operator for dihedral groups
• Weighted inequalities and uncertainty principles for the (k,a)-generalized Fourier transform
• The kernel of the radially deformed Fourier transform
• Laguerre semigroup and Dunkl operators
• Lauricella and Humbert functions through probabilistic tools
• Pitt's Inequalities and Uncertainty Principle for Generalized Fourier Transform
• A positive radial product formula for the Dunkl kernel
• A new product formula involving Bessel functions

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