GENERALIZED INTEGRAL TRANSFORMATIONS

This authoritative book explores in depth recent generalizations of some of the simpler, more commonly encountered integral transformations, in particular the Laplace, Mellin, Hanke, K, Weierstrass and convolution transformations, as well as those that arise from a variety of orthonormal series expansions.

Addressing graduate-level students of both mathematics and engineering, the author devotes a substantial part of the book to applications of generalized integral transformations to various initial-value and boundary-value problems, as well as to certain problems in system theory. The major emphasis of the work, however, is on the theory of these transformations.

The book begins with a consideration of countable multinormed spaces, countable union spaces, and their duals, then discusses distributions and generalized functions. Then, beginning with the two-sided Laplace, if takes up each of the integral transformations, ending with applications of the finite Hankel transformation of the first form (a Dirichlet problem for a semi-infinite cylinder) and the second form (heat flow in an infinite cylinder with a radiation condition).