Solvability of Riemann Boundary Value Problems and Applications to Approximative Properties of Perturbed Exponential System in Orlicz Spaces
Azerbaijan Journal of Mathematics, vol.14, no.1, pp.164-185, 2024 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 14 Issue: 1
- Publication Date: 2024
- Doi Number: 10.59849/2218-6816.2024.1.164
- Journal Name: Azerbaijan Journal of Mathematics
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
- Page Numbers: pp.164-185
- Keywords: approximative properties, Hardy-Orlicz classes, Orlicz space, Riemann boundary value problems
- Open Archive Collection: AVESIS Open Access Collection
- Yıldız Technical University Affiliated: Yes
Abstract
This work deals with the Orlicz space and the Hardy-Orlicz classes of analytic functions, generated by its norm. Non-homogeneous Riemann boundary value problem with piecewise Hölderian coefficient is considered in these classes. Based on N-function, we introduce new characteristic of Orlicz space and establish its relationship with the Boyd indices of considered Orlicz space. In terms of this characteristic and corresponding Boyd indices, we find a sufficient condition on the jumps of the argument of coefficient for solvability of Riemann boundary value problem in Hardy-Orlicz space and we construct a general solution. The obtained results are applied to establish the approximative properties (completeness, minimality, basicity) of a linear phase exponential system for corresponding Orlicz space.