Various operators among Hilbert spaces through integral transforms
by
Saburou Saitoh
Gunma University

For functional Hilbert spaces, we shall consider their linear and nonlinear transforms and we assume that their images are functions on a same set. For the images, we can introduce many operators such as sum, product, derivative and integral. By considering some inversions of the results of the operators, we shall introduce the corresponding operators for the functional Hilbert spaces. As a prototype example, we can consider the convolution which is a fundamental operator in analysis, because, the images of the convolution by the integral transform are mapped to the product of the images of the integral transform. For this idea, we shall show a background general theory and concrete examples, using concrete integral transforms. We shall refer to some concrete applications of the idea to norm inequalities and nonlinear integral equations.

Date received: May 17, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahk-60.