New Type Paley-Wiener Theorems for the Modified Multidimensional Mellin Transform.
Spectrum of Signals.
Convolution of Hankel transform and its application to an integral involving Bessel functions of first kind.
Integral representations of generalized Lauricella hypergeometric functions.
Integral transforms of Fourier cosine and sine generalized convolution type.
Inverse Problem for Fractional Diffusion Equation
MSC 2010: 26A33, 33E12, 34K29, 34L15, 35K57, 35R30 We prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements....
-function with complex parameters. I: Existence.
Reverse convolution inequalities and applications to inverse heat source problems.
Convolution inequalities and applications.
-function with complex parameters. II: Evaluation.
Reverse weighted - norm inequalities in convolutions.
Generalized Convolution Transforms and Toeplitz Plus Hankel Integral Equations
Mathematics Subject Classification: 44A05, 44A35 With the help of a generalized convolution and prove Watson’s and Plancherel’s theorems. Using generalized convolutions a class of Toeplitz plus Hankel integral equations, and also a system of integro-differential equations are solved in closed form.
A Generalized Convolution with a Weight Function for the Fourier Cosine and Sine Transforms
A generalized convolution with a weight function for the Fourier cosine and sine transforms is introduced. Its properties and applications to solving a system of integral equations are considered.
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