## Doctoral Dissertations

#### Title

Sets of interpolation for Fourier transforms of Frechet measures

January 1998

Mathematics

Ph.D.

#### Abstract

We extend various types of interpolation sets for Borel measures on T, e.g. Sidon sets and $\Lambda(p)$-sets, to Frechet measures on products of T. The Grothendieck Inequality and Grothendieck Factorization Theorem prove to be invaluable tools in the analysis of harmonic-analytic properties of bounded bilinear forms on $C({\bf T}) \times C({\bf T}).$ The push to dimensions higher than two uncovers interesting difficulties and obstacles which correspond in some sense to those encountered when one attempts to extend the Grothendieck Inequality and Factorization Theorem to dimensions higher than two. ^

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