On the Fine Structure of Spectra of Upper Triangular Double-Band Matrices as Operators on ℓp Spaces

In the present paper, we study the fine structure of spectra of infinite upper triangular double-band matrices as operators on ℓp, where 1 ≤ p \u3c ¥. Three methods for classifying the spectrum are considered. Moreover, the obtained results are used to study the eigenvalue problem associated with certain infinite matrices. Our results improve and generalize many known results in the current literature

Basis Properties of Exponential Systems With Linear Phases in Morrey-Sobolev Type Spaces

This paper is devoted to the study of basis properties of the system {t} ∪n e i(n+βsignn)t o n∈Z , where β is a real parameter, in Morrey-Sobolev-type spaces. We find sufficient conditions for the basicity in Morrey-Sobolev-type spaces in terms of inequalities of the parameter β