TENSOR PRODUCT DECOMPOSITION OF SOBOLEV SPACES AND CLASS OF p-NUCLEAR OPERATORS

摘要

In this work, tensor product decomposition method of Sobolev spaces is presented. Elements of applied functional analysis and a theory of cross-spaces are used. Many algebraic-topological identifications and the corresponding continuous injections for the Sobolev spaces are presented. Two main results are obtained : The separation of variables for every multi-variable function and the representation of every p-nuclear operator by one and only one function and vice-versa.