Generalized Eigenfunction Expansions for Operator Algebras

Generalized Eigenfunction Expansions for Operator Algebras^)

A generalized eigenfunction expansion may be regarded as a representation for the spectral theorem by a transform technique. These representations have been presented in many forms, an early version of which was the von Neumann "direct integral" decomposition for a class of operator algebras [l9]. In 1953 [17], Mautner applied the von Neumann technique to the class of operators acting in an L2-...

Convergence of Generalized Eigenfunction Expansions

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 hyperboli...

On the Localization Eigenfunction Expansions Associated with the Schrodinger Operator

In this paper we study eigenfunction expansions associated with the Schrodinger operator with a singular potential. In the paper it is obtained sufficient conditions for localization and uniformly convergence of the regularizations of the corresponding expansions

Perturbation of eigenfunction expansions.

A Uniqueness Theorem for Eigenfunction Expansions.

the series on the right of (3) being called the Fourier Eigenfunction Series and a. the Fourier Coefficients of f(x, y). I have studied elsewhere' the problem of convergence and summability of a Fourier Eigenfunction Series. In this note I am interested in announcing a result on uniqueness of eigenfunction expansion. Actually, we have thfe following, THEOREM. Let us suppose we are given an eige...