Orlov I. Scales of spaces as a means of linear and nonlinear analysis in locally convex spaces

Українська версія

Thesis for the degree of Doctor of Science (DSc)

State registration number

0505U000358

Thesis Registration Form

0505U000358.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

14-06-2005

Specialized Academic Board

Д 26.206.01

The Institute of Mathematics of NASU

Essay

Thesis deals with the formation and application of the means of analysis in the scales of locally convex spaces (LCS) to the problems of linear and nonlinear analysis in LCS. A number of main principles of functional analysis is transferred over the inductive scales of LCS. The normal decompositions of the dual spaces and operator spaces over LCS are studied. The differential calculus in LCS is essentially modified. A theory of extremums, a theory of K-differentiable mappings and K-extremums in LCS are constructed. The K-extremum conditions of the Euler-Lagrange functional in LCS are founded.

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