Displaying similar documents to “Weierstrass transform associated with the Hankel operator.”

Hankel Transform in Quantum Calculus and Applications

Haddad, Meniar (2006)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 44A15, 33D15, 81Q99 This paper is devoted to study the q-Hankel transform associated with the third q-Bessel function called also Hahn-Exton function. We use the q- approximation of unit for establishing a q-inverse formula of this transform. Moreover, we establish the related q-Parseval theorem.

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

Yurii Luchko, Virginia Kiryakova (2000)

Banach Center Publications

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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...

Hilbert transform and singular integrals on the spaces of tempered ultradistributions

Andrzej Kamiński, Dušanka Perišić, Stevan Pilipović (2000)

Banach Center Publications

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The Hilbert transform on the spaces S ' * ( R d ) of tempered ultradistributions is defined, uniquely in the sense of hyperfunctions, as the composition of the classical Hilbert transform with the operators of multiplying and dividing a function by a certain elliptic ultrapolynomial. We show that the Hilbert transform of tempered ultradistributions defined in this way preserves important properties of the classical Hilbert transform. We also give definitions and prove properties of singular integral...

An Analogue of Beurling-Hörmander’s Theorem for the Dunkl-Bessel Transform

Mejjaoli, Hatem (2006)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: Primary 35R10, Secondary 44A15 We establish an analogue of Beurling-Hörmander’s theorem for the Dunkl-Bessel transform FD,B on R(d+1,+). We deduce an analogue of Gelfand-Shilov, Hardy, Cowling-Price and Morgan theorems on R(d+1,+) by using the heat kernel associated to the Dunkl-Bessel-Laplace operator.

On q-Laplace Transforms of the q-Bessel Functions

Purohit, S., Kalla, S. (2007)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 33D15, 44A10, 44A20 The present paper deals with the evaluation of the q-Laplace transforms of a product of basic analogues of the Bessel functions. As applications, several useful special cases have been deduced.

Spectrum of Functions for the Dunkl Transform on R^d

Mejjaoli, Hatem, Trimèche, Khalifa (2007)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 42B10 In this paper, we establish real Paley-Wiener theorems for the Dunkl transform on R^d. More precisely, we characterize the functions in the Schwartz space S(R^d) and in L^2k(R^d) whose Dunkl transform has bounded, unbounded, convex and nonconvex support.

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.