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...

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-...

Direct simulation methods of Electron Paramagnetic Resonance (EPR) spectra are an alternative to standard eigenfunction-based approaches. Both methods can be employed to find numerical solutions of the Stochastic Liouville Equation (SLE) in order to compute spectral lineshapes. It can be shown rigorously that the domain of validity of eigenfunction expansion solutions of the SLE covers only a l...