A completeness criterion for a double power system with degenerate coefficients

Basicity of a system of exponents with a piecewise linear phase in Morrey-typespaces

“…To establish the basicity of the exponential system (1.1) for Morrey-type spaces M p,α , we will use the method of Riemann boundary value problems developed by Bilalov (see, e.g., [2,3,7,8,[10][11][12][13][14]). Consider the following homogeneous Riemann problem Introduce the following piecewise analytic functions on the complex plane cut byγ :…”

“…The latter idea originated from Bitsadze [15], later to be successfully used in [25,27,34]. Further development of this approach, used in establishing basis properties of perturbed trigonometric systems and power systems, was by Bilalov [2,3,7,11,14]. Similar problems are studied in [32,38].…”

Some properties of convolution in symmetric spaces and approximate identity

“…Recent years have seen an increased interest in di¤erent function spaces, such as Lebesgue spaces with variable summability index, Orlicz spaces, Morrey spaces, grand-Lebesgue spaces, etc. Some problems of harmonic analysis and approximation theory have been considered in [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Basicity of the classical exponential system, as well as its perturbations in the subspaces of Morrey space of functions de…ned on [ ; ] was investigated in [6,11,13,15] by the method of boundary value problems for analytic functions on a complex domain.…”

Comment on “On the Frame Properties of Degenerate System of Sines”

“…The basis properties (completeness, minimality, and Schauder basicity) of systems of the form { ( ) ( )}, where { ( )} is an exponential or trigonometric (cosine or sine) system, are investigated in several papers (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]). For example, Babenko gave an example {| | ⋅ int } ∈ , where | | < 1/2 and ̸ = 0, answering in the affirmative a question of Bari [16] on the existence of normalized basis for 2 (− , ) that is not a Riesz basis [2].…”

“…where ≥ 1, have been investigated in several papers (see, e.g., [1,[3][4][5][6][7][8][9][10][11][12][13][14][15]).…”