Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 71, pp. 1-19.

Title: Convergence of generalized eigenfunction expansions

Author: Mayumi Sakata (William Jewell College, Liberty, MO, USA)

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.