Constructing Finite Frames with Fractional Elliptic Bounded Value Problem and Singular Value Inequalities

Abstract

The existence and non-existence results for semilinear cooperative elliptic Systems for a class of fractional elliptic boundary value problems and constructor finite frames with a given frame operator are given .We construct the fractional Laplacian phase transitions, boundary reactions and the Brezis-Nirenberg type problem involving the square root of the laplacian. We show the singular values of a product of operators, of difference of positive semidefinite matrices, inequalities of matrices and for commutator operators .We obtain the deficits and excesses of finite normalized tight frames , optimal frames and constructing finite frames of a given spectrum and set of lengths. Inequalities for sums and direct sums of Hilbert space operators and matrix arithmetic–geometric mean are presented.For a class of fractional elliptic boundary value problems.