PROPERTIES AND DESCRIPTION OF SOLUTION SETS OF LINEAR FUNCTIONAL EQUATIONS ON A SIMPLE SMOOTH CURVE-Reference-Cited by-同舟云学术

PROPERTIES AND DESCRIPTION OF SOLUTION SETS OF LINEAR FUNCTIONAL EQUATIONS ON A SIMPLE SMOOTH CURVE

Published:2023 Issue:4 Volume:15 Page:5-13
ISSN:2075-809X
Container-title:Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics"
language:
Short-container-title:MMPh

Author:

Dilman V.L.^ORCID,

Abstract

The article investigates linear functional equations given in the field of complex numbers on simple smooth curves with a shift function of infinite order. The shift function has a nonzero derivative satisfying the Helder condition, and fixed points only at the ends of the curve. The paper gives a complete description of the sets of solutions of such equations in the classes of continuous, Helder, and primitive Lebesgue functions with a coefficient and the right side of the same classes, depending on the values of the coefficient of the equation at the ends of the curve. Sufficient conditions have been established for the solutions to belong to the specified functional classes.

Publisher

FSAEIHE South Ural State University (National Research University)

Subject

General Medicine

Reference21 articles.

1. 1. Chi riko a .I., leshchinski .B. Integral Equations with Generalized Logarithmic and Power Kernels. Soviet Mathematics (Izvestiya VUZ. Matematika), 1976, Vol. 20, no. 6, pp. 80-92.

2. 2. Dil'man V.L., Chibrikova L.I. Solutions of an Integral Equation with Generalized Logarithmic Kernel in Lp, p > 1. Soviet Mathematics (Izvestiya VUZ. Matematika), 1986, Vol. 30, no. 4, pp. 33-46.

3. 3. Litvinchuk G.S. Solvability Theory of Boundary Value Problems and Singular Integral Equations with Shift. Springer Science+Business Media Dordrecht, 2012, 378 p. DOI: 10.1007/978-94-011- 4363-9

4. 4. Kravchenko V.G., Litvinchuk G.S. Introduction to the Theory of Singular Integral Operators with Shift. Springer Science+Business Media, 2012, 288 p. DOI: 10.1007/978-94-011-1180-5

5. 5. Karlovich Yu.I., Kravchenko V.G., Litvinchuk G.S. Noether's Theory of Singular Integral Operators with Shift. Soviet Mathematics (Izvestiya VUZ. Matematika), 1983, Vol. 27, no. 4, pp. 1-34.

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