Solvability of Riemann Boundary Value Problems and Applications to Approximative Properties of Perturbed Exponential System in Orlicz Spaces

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Bilalov B. T., SEZER Y., Alizadeh F. A., Ildiz U.

Azerbaijan Journal of Mathematics, vol.14, no.1, pp.164-185, 2024 (ESCI) identifier

  • 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
  • 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.