Pseudoshift and the Fundamental Solution of the Kipriyanov -Operator

Solutions of singular differential equations with the Bessel operator of negative order are studied. In this regard, of great interest are the solutions of the singular differential Bessel equation , which are presented in the paper as linearly independent functions and , . Some properties of the fu...

Full description

Saved in:
Bibliographic Details
Published inDifferential equations Vol. 58; no. 12; pp. 1639 - 1650
Main Authors Lyakhov, L. N., Bulatov, Yu. N., Roshchupkin, S. A., Sanina, E. L.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.12.2022
Springer
Springer Nature B.V
Subjects
Difference and Functional Equations
Differential equations
Euclidean geometry
Half spaces
Mathematics
Mathematics and Statistics
Operators (mathematics)
Ordinary Differential Equations
Partial Differential Equations
Singularity (mathematics)
Online AccessGet full text

Cover

More Information
Summary:Solutions of singular differential equations with the Bessel operator of negative order are studied. In this regard, of great interest are the solutions of the singular differential Bessel equation , which are presented in the paper as linearly independent functions and , . Some properties of the functions expressed in terms of the properties of the Bessel–Levitan -function are considered. The direct and inverse -Bessel transforms are introduced, and the -pseudoshift operator that commutes with the Bessel operator is defined. The fundamental solution of the ordinary singular differential operator is found. A representation of the fundamental solution of the Kipriyanov -operator with a singularity at the point and on the cone in the Euclidean -dimensional half-space is given.
ISSN:0012-2661
1608-3083
DOI:10.1134/S00122661220120072