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Applications of entire function theory to an imbedding theorem for differentiable functions of several real variables

University of British Columbia

The subject of this thesis is the fractional order Sobolev space, H[superscript]r[subscript]p, as considered by Nikol'skii; the goal is to demonstrate an imbedding theorem for H[superscript]r[subscript]p analogous to the classical imbedding theorem for W[superscript]m[subscript]p which was first shown by Sobolev. The properties established here for spaces H[superscript]r[subscript]p defined over all of Rn, including completeness and imbedding theorems, are demonstrated by a technique involving the approximation of functions in those spaces by entire functions of the exponential type. Properties of such entire functions, which are of interest in theire own right, are developed in a separate chapter. An extension theorem for differentiable developed in a separate chapter. An extension theorem for differentiable functions defined over an open subset of Rn is also proved.

Text

2011-03-17

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http://hdl.handle.net/2429/32552

Mathematics

University of British Columbia

Graduate