Sakata, Mayumi2021-08-062021-08-062007-05-15Sakata, M. (2007). Convergence of generalized eigenfunction expansions. <i>Electronic Journal of Differential Equations, 2007</i>(71), pp. 1-19.1072-6691https://hdl.handle.net/10877/14233We 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.Text19 pages1 file (.pdf)enAttribution 4.0 InternationalGeneralized eigenfunction expansionGeneralized eigenprojectionFourier transformDifferential operatorsHecke operatorsModular groupArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.