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.
