Convergence of generalized eigenfunction expansions
Date
2007-05-15
Authors
Sakata, Mayumi
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
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.
Description
Keywords
Generalized eigenfunction expansion, Generalized eigenprojection, Fourier transform, Differential operators, Hecke operators, Modular group
Citation
Sakata, M. (2007). Convergence of generalized eigenfunction expansions. <i>Electronic Journal of Differential Equations, 2007</i>(71), pp. 1-19.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.