A new form of the spherical expansion of zonal functions and Fourier transforms of -finite functions.

Bezubik, Agata; Strasburger, Aleksander

Displaying similar documents to “A new form of the spherical expansion of zonal functions and Fourier transforms of $SO (d)$ -finite functions.”

External ellipsoidal harmonics for the Dunkl-Laplacian.

Volkmer, Hans (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Generalized ellipsoidal and sphero-conal harmonics.

Volkmer, Hans (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Inversion formulas for the spherical Radon-Dunkl transform.

Li, Zhongkai, Song, Futao (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Liouville theorem for Dunkl polyharmonic functions.

Ren, Guangbin, Liu, Liang (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Twisted spherical means in annular regions in $ℂ^{n}$ and support theorems

Rama Rawat, R.K. Srivastava (2009)

Annales de l’institut Fourier

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Let $Z (Ann (r, R))$ be the class of all continuous functions $f$ on the annulus $Ann (r, R)$ in $ℂ^{n}$ with twisted spherical mean $f \times μ_{s} (z) = 0,$ whenever $z \in ℂ^{n}$ and $s > 0$ satisfy the condition that the sphere $S_{s} (z) \subseteq Ann (r, R)$ and ball $B_{r} (0) \subseteq B_{s} (z) .$ In this paper, we give a characterization for functions in $Z (Ann (r, R))$ in terms of their spherical harmonic coefficients. We also prove support theorems for the twisted spherical means in $ℂ^{n}$ which improve some of the earlier results.

Spherical harmonics and spherical averages of Fourier transforms

Per Sjölin (2002)

Rendiconti del Seminario Matematico della Università di Padova

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On the Range of the Fourier Transform Associated with the Spherical Mean Operator

Jelassi, M., Rachdi, L. (2004)

Fractional Calculus and Applied Analysis

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We characterize the range of some spaces of functions by the Fourier transform associated with the spherical mean operator R and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schawrtz theorems.

Spherical means on the Heisenberg group and a restriction theorem for the symplectic Fourier transform.

Sundaram Thangavelu (1991)

Revista Matemática Iberoamericana

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The aim of this paper is to study mean value operators on the reduced Heisenberg group H/Γ, where H is the Heisenberg group and Γ is the subgroup {(0,2πk): k ∈ Z} of H.

Integrals involving Hermite polynomials, generalized hypergeometric series and Fox's H-function, and Fourier-Hermite series for products of generalized hypergeometric functions

Sadhana Mishra (1991)

Annales Polonici Mathematici

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We evaluate an integral involving an Hermite polynomial, a generalized hypergeometric series and Fox's H-function, and employ it to evaluate a double integral involving Hermite polynomials, generalized hypergeometric series and the H-function. We further utilize the integral to establish a Fourier-Hermite expansion and a double Fourier-Hermite expansion for products of generalized hypergeometric functions.

Displaying similar documents to “A new form of the spherical expansion of zonal functions and Fourier transforms of SO ( d ) -finite functions.”

Displaying similar documents to “A new form of the spherical expansion of zonal functions and Fourier transforms of $SO (d)$ -finite functions.”