Restrictions and Extensions of RKHSs by Means of Bounded Linear Operators Using the Tikhonov Regularization (Research on real, complex and functional analysis from the perspective of function spaces)

Abstract

In this note, we shall consider the estimates of the norms of reproducing kernel Hilbert spaces on a domain and on its subset, and at the same time, restrictions and extensions of the functions by means of bounded linear operators using the Tikhonov regularization. Here, the Bergman spaces and Sobolev Hilbert spaces may be considered as typical examples and the method will have a general nature for reproducing kernel Hilbert spaces (RKHSs). We see many open problems and the up-to-date related information.