The Questions of Uniqueness for Franklin Series
Ministry of Education and Science of RA, State Committee of Science Contracts (thematic) funding competition in 2015, a field, Mathematics

Short description

The orthonormal system introduced in 1928 by Ph. Franklin has been a subject of many-sided investigation for the last fifty years. Some questions posed by S. Banach were answered applying that system (the existence of a basis in the space of analytic functions on the unit disc continuous on the closed disc, the existence of basis in the space of differentiable functions of two variables). The unconditionality of this system in Lebesgue reflexive spaces is also proved. Nevertheless the uniqueness questions for Franklin series have not been deeply investigated. Until recently it was unknown whether a Cantor type theorem is true for Franklin series. The result concerning this question without proofs was announced by G. Gevorkyan. A lot of questions arise concerning this result, which are stated in the project. These questions will be investigated within the frameworks of the project.

Project Manager
Gegham G. Gevorgyan, Doctor of Phys. Math. Sciences, Professor

Staff members

Karen A. Keryan, Ph.D

Tel.: (+374 10) 554702
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