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2012•Siberian Mathematical JournalRequires access

Some properties and applications of the integrodifferential operators of hadamard-marchaud type in the class of harmonic functions

Abdumauvlen Suleimanovich Berdyshev, Batirkhan Turmetov, Bakhtiyar Jalilovich Kadirkulov

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Abstract

In the class of harmonic functions, we study the properties of some integrodifferential operators generalizing the operators of fractional derivation in the sense of Hadamard and Hadamard-Marchaud. By way of application of the so-obtained properties, we consider some boundary value problems for the Laplace equation in the ball.

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What this paper is about

In the class of harmonic functions, we study the properties of some integrodifferential operators generalizing the operators of fractional derivation in the sense of Hadamard and Hadamard-Marchaud. By way of application of the so-obtained properties, we consider some boundary value problems for the Laplace equation in the ball.

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OpenAlex reports 14 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In the class of harmonic functions, we study the properties of some integrodifferential operators generalizing the operators of fractional derivation in the sense of Hadamard and Hadamard-Marchaud. By way of application of the so-obtained properties, we consider some boundary value problems for the Laplace equation in the ball.

Key concepts: Hadamard transform, Mathematics, Harmonic function, Hadamard three-lines theorem, Laplace transform, Hadamard three-circle theorem, Class (philosophy), Boundary value problem

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