Sharp Bounds for the Operator Norm of the Mehler Kernel Operator

Author: Deutsch, Leslie Joseph

Year: 1981

Degree: Dissertation (Ph.D.)

Advisor: Luxemburg, W. A. J.

Committee Member: Unknown, Unknown

Option: Mathematics

DOI: 10.7907/zcm4-w140

Abstract

In this thesis the norms of the Mehler kernel operators are calculated. In particular, Babenko's conjecture about the norms of these operators with purely imaginary parameter is settled. The proof is inspired by Wiener's approach to Fourier theory and his proof of Plancherel 's theorem. An account is given of Wiener's approach, as well as of the important tools and theorems, particularly those of Beckner, needed to prove the main result. Applications to Kober operators and smoothing operators are given.

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