William Jewell College
500 College Hill, Box 1108
Liberty, MO 64068-1896, USA
email: sakatam@william.jewell.edu
Mayumi Sakata
Abstract:
We present a simplified theory of generalized eigenfunction expansions
for a commuting family of bounded operators and with finitely many
unbounded operators. We also study the convergence of these expansions,
giving an abstract type of uniform convergence result, and illustrate
the theory by giving two examples: The Fourier transform on Hecke
operators, and the Laplacian operators in hyperbolic spaces.
Submitted March 6, 2007. Published May 15, 2007.
Math Subject Classifications: 46L10, 47E05, 47F05, 47B25, 11F25, 11F03.
Key Words: Generalized eigenfunction expansion;
Generalized eigenprojection; Fourier transform; differential operators,
Hecke operators; modular group.
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Mayumi Sakata William Jewell College 500 College Hill, Box 1108 Liberty, MO 64068-1896, USA email: sakatam@william.jewell.edu |
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