Functional Analysis and Applications Seminar 

30/04/2010, 15:00 — 16:00 — Room P3.10, Mathematics Building
Saburou Saitoh, Gunma University, Tokyo, Japan, and University of Aveiro, Portugal

Bounded linear operator equations and discretization by using the theory of reproducing kernels

In this seminar, I first would like to introduce some fundamental theory for linear transforms in the framework of Hilbert spaces and its general applications with very concrete typical examples. Secondly, I will propose a new method for inversions of bounded linear operators on Hilbert spaces with discretization. The contents will be given by the following key words: Reproducing kernel, Pythagorean theorem, inversion of the linear systems, inverse problem, inverse heat conduction, real inversion of the Laplace transform, analytic extension, observation data, non-linear system, non-linear transform, generalized inverse, Tikhonov regularization, singular integral equations.