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Theory of reproducing kernels for Hilbert spaces of vector valued functions
Pedrick, George
Pedrick, George
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Abstract
The general theory of reproducing kernels developed by N. Aronszajn provides a unifying point of view for the study of an important class of Hilbert spaces of real or complex valued functions and for the appliĀcation of the methods of Hilbert space theory to different problems in the theory of partial differential equations. With a view to applications to systems of such equations the form which the theory takes in the case of spaces of vector valued functions was invesĀtigated, initially for finite dimensional and Hilbert range spaces. It was found that the natural setting for such a generalization of the theory is that
in which the functions of the functional Hilbert space take their values in an arbitrary locally convex linear topological space, since all of the main reĀsults are essentially preserved in that setting and a more special case would restrict unduly the applications. The present study is confined to the exposition of the general theory with a few illustrations and undertakes to extend the basic notions of proper functional space, reproducing kernel and positive matrix and their properĀ ties as they occur in the paper of N. Aronszajn.
Description
1 v. ; 29 cm. Includes bibliographical references.
Date
1957
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Publisher
University of Kansas
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Keywords
Hilbert space, Vector valued functions