Eigenfunction expansions for partially hypoelliptic operators

Eigenfunction Expansions for Schrödinger Operators on Metric Graphs

We construct an expansion in generalized eigenfunctions for Schrödinger operators on metric graphs. We require rather minimal assumptions concerning the graph structure and the boundary conditions at the vertices.

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.

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...