The Transmutation Method and Boundary-Value Problems for Singular Differential Equations

Abstract

The main content of this book is composed from two doctoral theses: by V.\,V.~Katrakhov (1989) and by S.\,M.~Sitnik (2016). In our work, for the first time in the format of a monograph, we systematically expound the theory of transmutation operators and their applications to differential equations with singularities in coefficients, in particular, with Bessel operators. Along with detailed survey and bibliography on this theory, the book contains original results of the authors. Significant part of these results is published with detailed proofs for the first time. The book is concluded with a brief biographic essay about Valeriy V.~Katrakhov, as well as detailed bibliography containing 648 references.