An Introduction to the Theory of Reproducing Kernel Hilbert Spaces
نویسندگان
چکیده
These notes give an introduction to the theory of reproducing kernel Hilbert spaces and their multipliers. We begin with the material that is contained in Aronszajn’s classic paper on the subject. We take a somewhat algebraic view of some of his results and discuss them in the context of pull-back and push-out constructions. We then prove Schoenberg’s results on negative definite functions and his characterization of metric spaces that can be embedded isometrically in Hilbert spaces. Following this we study multipliers of reproducing kernel Hilbert spaces and use them to give classic proofs of Pick’s and Nevanlinna’s theorems. In later chapters we consider generalizations of this theory to the vector-valued setting.
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