Transmutation Operators as a Solvability Concept of Abstract Singular Equations

Abstract

One of the methods of studying differential equations is the transmutation operators method. Detailed study of the theory of transmutation operators with applications may be found in the literature. Application of transmutation operators establishes many important results for different classes of differential equations including singular equations with Bessel operator. In this paper transmutation operators are used in more general case when in Euler–Poisson–Darboux equation as the space-variable Laplace operator is replaced by some abstract operator acting in Banach space. Also some other abstract singular equations are studied by this method.