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GENERALIZED INTEGRAL TRANSFORMATIONS |
| SHORT DESCRIPTION OF THE BOOK This book explores in depth distributional generalizations of some of the more commonly encountered integral transformations, in particular the Laplace, Mellin, Hankel, K, Weierstrass, and convolution transformations, as well as those that arise from a variety of orthonormal series expansions. It is written at the graduate level, and a substantial part of it is devoted to applications of generalized integral transformations to various initial-value and boundary-value problems, as well as to certain problems in systems theory. The major emphasis of the work, however, is on the theory of these transformations. The book begins with a consideration of countably multinormed spaces, countable union spaces, and their duals, and then discusses distributions and generalized functions. Next, beginning with the two-sided Laplace transformation, it takes up each of the integral transformations and provides applications to physical problems throughout. The book is written at the graduate level and assumes some knowledge of Lebesgue integration and of functions of a complex variable. |
