ON THE CONVERGENCE OF SOME EIGENFUNCTION EXPANSIONS

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...

Eigenfunction Expansions for Some Nonselfadjoint Operators and the Transport Equation*

There are many papers dealing with various aspects of the perturbation theory of a continuous spectrum [l-5, 12-151. In [3-51 some problems with nonselfadjoint operators were considered. In [3b] conditions for the perturbed operator to be similar to the unperturbed one are given. In [4] the Schrijdinger operator with a complex-valued potential was considered. In [S ] a theorem is announced in w...

Perturbation of eigenfunction expansions.

Eigenfunction Expansions and Transformation Theory

Generalized eigenfunctions may be regarded as vectors of a basis in a particular direct integral of Hilbert spaces or as elements of the antidual space Φ× in a convenient Gelfand triplet Φ ⊆ H ⊆ Φ×. This work presents a fit treatment for computational purposes of transformations formulas relating different generalized bases of eigenfunctions in both frameworks direct integrals and Gelfand tripl...

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