http://hdl.handle.net/20.500.12323/6831 Sat, 18 Apr 2026 21:33:52 GMT 2026-04-18T21:33:52Z http://localhost:80/jspui/retrieve/acedd113-72f2-4416-bfc0-5bcad46ff39c/publication-icon-3.jpg http://hdl.handle.net/20.500.12323/6831 http://hdl.handle.net/20.500.12323/6846 Title: Basis Properties of Some Systems In Banach Spaces Authors: Huseynli, Ali A. Abstract: Let uˆn = (un, an), n = 1, 2, ... be some complete and minimal system of vectors in X = X 0 ⊕ C m and let ϑˆ n = (ϑn, bn), n = 1, 2, ... be corresponding biorthogonal system. N is a set of natural numbers, J = {n1, ..., nm} ⊂ N is some set of different and natural numbers, n0 = N \J, bn = (βn1 , ..., βnm), δ = det βnkj m k,j=1. In the present paper it is shown that in case of δ = 0 statement on non-minimality of the system {un}n∈N0 in the space X0, in generally, is not true, and sufficient conditions are cited when this statement becomes true. Mon, 01 Jan 2007 00:00:00 GMT http://hdl.handle.net/20.500.12323/6846 2007-01-01T00:00:00Z http://hdl.handle.net/20.500.12323/4594 Title: Some properties of defect bases and bases of subspaces Authors: Huseynli, Ali A. Abstract: In the paper we study some properties of defect bases in Banach spaces and some closeness theorems for basicity of systems of subspaces of Banach spaces is proved. Tue, 01 Jan 2008 00:00:00 GMT http://hdl.handle.net/20.500.12323/4594 2008-01-01T00:00:00Z http://hdl.handle.net/20.500.12323/4593 Title: Riemann boundary value problems in generalized weighted hardy spaces Authors: Bilalov, Bilal T.; Huseynli, Ali A.; Seyidova, Fidan Sh. Abstract: Riemann boundary value problem of analytic function theory in weighted Hardy classes with variable summability index is considered in this work. The Fredholmness of this problem is investigated under certain conditions on coefficients and a weight. The general solution for homogeneous problem is obtained in weighted Hardy classes with variable summability index. In the case where the weight function satisfies the Muckenhoupt condition with variable summability index, the solvability of the non-homogeneous Riemann problem with the right side from the generalized weighted Lebesgue space is studied. Sun, 01 Jan 2017 00:00:00 GMT http://hdl.handle.net/20.500.12323/4593 2017-01-01T00:00:00Z http://hdl.handle.net/20.500.12323/4592 Title: Lp;r spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework Authors: Huseynli, Ali; Mirzabalayeva, Asmar Abstract: In the present work the space Lp;r which is continuously embedded into Lp is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is bounded in { Lp;r. The problem of basisness of the system A (t) e int; B (t) e −int} n∈Z+ , is also considered. It is shown that under an additional condition this system forms a basis in Lp;r if and only if the Riemann-Hilbert problem has a unique solution in corresponding Hardy class H+ p;r × H+ p;r. Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/20.500.12323/4592 2019-01-01T00:00:00Z