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An integral analog of the Leibniz rule for the operators of fractional calculus was considered in paper [1]. These operators are known to belong to the class of convolution transforms [2]. It seems very natural to try to obtain some new integral analog of the Leibniz rule for other convolution operators. We have found a general method for constructing such integral analogs on the base of notion of G-convolution [4]. Several results obtained by this method are represented in this article.

The generalized Airy diffusion equation.

Cholewinski, Frank M., Reneke, James A. (2003)

Electronic Journal of Differential Equations (EJDE) [electronic only]

The generalized sampling theorem for transforms of not necessarily square integrable functions.

Jerri, A.J. (1985)

International Journal of Mathematics and Mathematical Sciences

The heat transform and its use in thermal identification problems for electronic circuits.

Kindermann, Stefan, Janicki, Marcin (2009)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

The Hilbert transform and maximal function along nonconvex curves in the plane.

James Vance, Stephen Wainger, James Wright (1994)

Revista Matemática Iberoamericana

In this paper we study the Hilbert transform and maximal function related to a curve in R2.

The Hilbert transform in weighted spaces of integrable vector-valued functions

T. M. Wolniewicz (1987)

Colloquium Mathematicae

The Identification Problem for the Constantly Attenuated Radon Transform.

Alexander Hertle (1988)

Mathematische Zeitschrift

The inversion formulae for some Bessel and hypergeometric

S. L. Kalla, S. E. de González de Galindo (1976)

Revista colombiana de matematicas

The $L^{2}$ -optimal convolving functions in reconstruction convolution algorithms

František Matúš (1987)

Kybernetika

The Lambert transform on $ε^{'} (I)$

Negrin, E.R. (1993)

Portugaliae mathematica

The link between the kernel method and the method of adjoints for the generalized index $_{2} F_{1}$ -transform

Benito J. González, Emilio R. Negrin (1996)

Commentationes Mathematicae Universitatis Carolinae

In this note we show that the two definitions of generalized index $_{2} F_{1}$ -transform given in the previous works [1] and [2] agree for distributions of compact support.

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Displaying 261 – 280 of 324

The continuous Legendre transform, its inverse transform, and applications.

The distributional 1F1-Transform.

The Dunkl transform.

The equivalence of two conditions for weight functions

The Fourier transforms of Lipschitz functions on the Heisenberg group.

The general chain transform and self-reciprocal functions.

The generalizations of integral analog of the Leibniz rule on the G-convolutions.