학술논문
Kipriyanov Singular Pseudodifferential Operators Generated by Bessel 핁-Transform.
Document Type
Article
Source
Subject
*PSEUDODIFFERENTIAL operators
*DIFFERENTIAL operators
*INTEGRAL transforms
*BESSEL functions
*EQUATIONS
*
*
*
*
Language
ISSN
1072-3374
Abstract
We introduce integral transforms to study problems for the singular Bessel differential operators B−γ with negative parameter −γ < 0. A solution to the singular Bessel equation B−γu+u = 0 is a function u = 핁μ expressed in terms of the Bessel functions of the first kind with positive parameter μ = (γ + 1)/2. Based on the notion of a 핋-pseudoshift, we formulate the Levitan addition theorem. We construct the Bessel 핁-transform and the corresponding class of singular 핁-pseudodifferential operators. We prove a theorem on the order of 핁-pseudodifferential operators in the class of Sobolev–Kipriyanov functions. [ABSTRACT FROM AUTHOR]