Doğuran çekirdekli Hilbert uzayları

In this thesis we make a survey of the theory of reproducing kernel Hilbert spacesassociated with positive definite kernels and we illustrate their applications for in-terpolation problems of Nevanlinna-Pick type. Firstly we focus on the propertiesof reproducing kernel Hilbert spaces, generation of new spaces and relationshipsbetween their kernels and some theorems on extensions of functions and kernels.One of the most useful reproducing kernel Hilbert spaces, the Bergman space, isstudied in details in chapter 3. After giving a brief definition of Hardy spaces, wededicate the last part for applications of interpolation problems of Nevanlinna-Pick type with three main theorems: interpolation with a finite number of points,interpolation with an infinite number of points and interpolation with points onthe boundary. Finally we include an Appendix that contains a brief recall of themain results from functional analysis and operator theory.Keywords: Reproducing kernel, Reproducing kernel Hilbert spaces, Bergmanspaces, Hardy spaces, Interpolation, Riesz theorem.i