In this paper, we prove the existence of a particular diagonalization for normal bounded operators defined on subspaces $$L^2({\mathfrak {S}})$$ where $${\mathfrak {S}}$$ is second countable LCA group. The act are invariant under action group $$\Gamma $$ which semi-direct product uniform lattice with discrete automorphisms. This class includes crystal groups important in applications as mode...

In this note, we solve the dynamical sampling problem for a class of shift-preserving operators L:V?V acting on finitely generated shift-invariant space V. We find conditions L and finite set functions V so that iterations operator produce frame generator This means integer translations generators form

Abstract The notion of the capacity a polynomial was introduced by Gurvits around 2005, originally to give drastically simplified proofs van der Waerden lower bound for permanents doubly stochastic matrices and Schrijver’s inequality perfect matchings regular bipartite graphs. Since this seminal work, has been utilised various combinatorial quantities polynomial-time algorithms approximate such...

in this paper, let $l$ be a completeresiduated lattice, and let {bf set} denote the category of setsand mappings, $lf$-{bf pos} denote the category of $lf$-posets and$lf$-monotone mappings, and $lf$-{bf cslat}$(sqcup)$, $lf$-{bfcslat}$(sqcap)$ denote the category of $lf$-completelattices and $lf$-join-preserving mappings and the category of$lf$-complete lattices and $lf$-meet-preserving mapping...

The Schrödinger operators with exchange terms for certain Calogero-Sutherland quantum many body systems have eigenfunctions which factor into the symmetric ground state and a multivariable polynomial. The polynomial can be chosen to have a prescribed symmetry (i.e. be symmetric or antisymmetric) with respect to the interchange of some specified variables. For four particular Calogero-Sutherland...

in present paper acertain convolution operator of analytic functions is defined.moreover, subordination- and superordination- preserving propertiesfor a class of analytic operators defined on the space of normalizedanalytic functions in the open unit disk is obtained. we also applythis to obtain sandwich results and generalizations of some knownresults.