Bergman S. Integral Operators in the Theory of Linear Partial Differential Equations

Springer, 1969. — 154 p.
The present book deals with the construction of solutions of linear partial differential equations by means of integral operators which transform analytic functions of a complex variable into such solutions. The theory of analytic functions has achieved a high degree of development and simplicity, and the operator method permits us to exploit thi s theory in the study of differential equations. Although the study of existence and uniqueness of solutions has been highly developed, much less attention has been paid to the investigation of function theoretical properties and to the explicit construction of regular and singular solutions using a unified general procedure. This book attempts to fill in the gap in this direction.