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

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 Ho center dot lderian 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.