In this note we study the structure of shift-preserving operators acting on a finitely generated shift-invariant space. We define new notion diagonalization for these operators, which call s-diagonalization. give necessary and sufficient conditions bounded operator in order to be s-diagonalizable. These are terms its range operator. also obtain generalized Spectral Theorem normal operators.

In the field of blind source separation, joint-diagonalization-based approaches constitute an important framework, leading to useful algorithms such as the popular joint approximate diagonalization of eigenmatrices (JADE) and simultaneous third-order tensor diagonalization (STOTD) algorithms. However, they are often restricted to the case of cumulants of order four. In this paper, we extend the...

Diagonalization in the spirit of Cantor’s diagonal arguments is a widely used tool in theoretical computer sciences to obtain structural results about computational problems and complexity classes by indirect proofs. The Uniform Diagonalization Theorem allows the construction of problems outside complexity classes while still being reducible to a specific decision problem. This paper provides a...

The Pseudopotential Algorithm for Real-Space Electronic Calculations (PARSEC) is a software package written by a team consisting of materials scientists and computer scientists over approximately one decade. During this period, the algorithms used in PARSEC have undergone a series of improvements. This paper reviews the nature of the eigenvalue problems encountered in solving the Kohn-Sham equa...