Valuations on Lp-spaces
by Tsang, Andy, Ph.D., POLYTECHNIC INSTITUTE OF NEW YORK UNIVERSITY, 2010, 102 pages; 3412566

Abstract:

Chapter 1 provides the preliminaries. In Chapter 2, the main result is a representation theorem for continuous valuations on Lp-spaces whose underlying measure is non-atomic. In Chapter 3, the results from Chapter 2 are used to characterize continuous translation invariant valuations on Lp([special characters omitted]). In Chapter 4, the results from Chapter 2 are used to characterize continuous rotation invariant valuations on Lp( Sn−1). In Chapter 5, a complete classification is obtained of continuous GL( n)-equivariant Minkowski valuations on Lp(μ n), where n ≥ 2, and μ n is a measure on [special characters omitted] defined as μn(E) = [special characters omitted]|x|dx, for Lebesgue measurable sets E. Chapter 6 has applications to the results from Chapters 2–5. Note that the results from Chapters 2–4 are published [32].
 
AdviserMonika Ludwig
SchoolPOLYTECHNIC INSTITUTE OF NEW YORK UNIVERSITY
SourceDAI/B 71-08, p. , Sep 2010
Source TypeDissertation
SubjectsMathematics
Publication Number3412566
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