New multiplier methods for summing classical eigenfunction expansions

Summing Logarithmic Expansions for Elliptic

Elliptic problems in a two-dimensional domain containing one or several small holes are studied asymptotically in the limit of small hole radius ". As a result of the perturbation , the asymptotic solution to this class of problems contains an innnite logarithmic expansion in powers of ?1= log ". A hybrid asymptotic-numerical technique is used to sum these innnite logarithmic expansions and to ...

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...

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 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...