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
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