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    Theory of reproducing kernels for Hilbert spaces of vector valued functions

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    Issue Date
    1957
    Author
    Pedrick, George
    Publisher
    University of Kansas
    Type
    Dissertation
    Degree Level
    Ph.D.
    Discipline
    Mathematics
    Rights
    This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.
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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 appli­cation 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 inves­tigated, 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 re­sults 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 proper­ ties as they occur in the paper of N. Aronszajn.
    Description
    1 v. ; 29 cm. Includes bibliographical references.
    URI
    http://hdl.handle.net/1808/18369
    Collections
    • Mathematics Dissertations and Theses [180]
    • Dissertations [4472]

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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