Open AccessOn Stability of Bases Made from Perturbed Exponential Systems in Morrey Type Spaces
Author(s) -
Fatima Guliyeva
Publication year - 2020
Publication title -
international journal of education and information technologies
Language(s) - English
Resource type - Journals
ISSN - 2074-1316
DOI - 10.46300/9109.2020.14.8
Subject(s) - mathematics , lp space , subspace topology , completeness (order theory) , pure mathematics , sequence (biology) , separable space , type (biology) , exponential function , basis (linear algebra) , mathematical analysis , discrete mathematics , banach space , geometry , ecology , biology , genetics
Perturbed exponential system {eiλkχ}keZ (where {λn} is some sequence of real numbers) isconsidered in Morrey spaces Lp,α (0, π) These spaces arenon-separable (except for exceptional cases), and thereforethe above system is not complete in them. Based on theshift operator, we define the subspace Mp,a (0, π)C Lp,α (0, π) where continuous functions aredense. We find a condition on the sequence {λn} which issufficient for the above system to form a basis for thesubspace Mp,a (0, π). Our results are the analogues ofthose obtained earlier for the Lebesgue spaces Lp. Wealso establish an analogue of classical Levinson theorem onthe completeness of above system in the spaces Lp,1 <= p <=+∞