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Hankel type integral transforms connected with the hyper-Bessel differential operators

Yurii Luchko, Virginia Kiryakova (2000)

Banach Center Publications

In this paper we give a solution of a problem posed by the second author in her book, namely, to find symmetrical integral transforms of Fourier type, generalizing the cos-Fourier (sin-Fourier) transform and the Hankel transform, and suitable for dealing with the hyper-Bessel differential operators of order m>1 B : = x - β j = 1 m ( x ( d / d x ) + β γ j ) , β>0, γ j R , j=1,...,m. We obtain such integral transforms corresponding to hyper-Bessel operators of even order 2m and belonging to the class of the Mellin convolution type transforms...

Harmonic analysis for spinors on real hyperbolic spaces

Roberto Camporesi, Emmanuel Pedon (2001)

Colloquium Mathematicae

We develop the L² harmonic analysis for (Dirac) spinors on the real hyperbolic space Hⁿ(ℝ) and give the analogue of the classical notions and results known for functions and differential forms: we investigate the Poisson transform, spherical function theory, spherical Fourier transform and Fourier transform. Very explicit expressions and statements are obtained by reduction to Jacobi analysis on L²(ℝ). As applications, we describe the exact spectrum of the Dirac operator, study the Abel transform...

Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms.

Aline Bonami, Demange, Bruno, Jaming, Philippe (2003)

Revista Matemática Iberoamericana

We extend an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all functions f on Rd which may be written as P(x)exp(-(Ax,x)), with A a real symmetric definite positive matrix, are characterized by integrability conditions on the product f(x)f(y). We then obtain similar results for the windowed Fourier transform (also known, up to elementary changes of functions, as the radar ambiguity function or the Wigner transform). We complete the paper with...

Hermite Series with Polar Singularities

Boychev, Georgi S. (2012)

Mathematica Balkanica New Series

MSC 2010: 33C45, 40G05Series in Hermite polynomials with poles on the boundaries of their regions of convergence are considered.

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