Department Chair, PhD in Mathematics http://hdl.handle.net/20.500.12323/6830 2026-04-18T19:53:35Z 2026-04-18T19:53:35Z Huseynli, Ali A. http://hdl.handle.net/20.500.12323/6846 2023-09-28T12:13:50Z 2007-01-01T00:00:00Z

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.

2007-01-01T00:00:00Z Huseynli, Ali A. http://hdl.handle.net/20.500.12323/4594 2023-09-28T12:15:18Z 2008-01-01T00:00:00Z

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.

2008-01-01T00:00:00Z Bilalov, Bilal T. Huseynli, Ali A. Seyidova, Fidan Sh. http://hdl.handle.net/20.500.12323/4593 2023-09-28T12:20:48Z 2017-01-01T00:00:00Z

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.

2017-01-01T00:00:00Z Huseynli, Ali Mirzabalayeva, Asmar http://hdl.handle.net/20.500.12323/4592 2023-09-28T12:21:27Z 2019-01-01T00:00:00Z

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.

2019-01-01T00:00:00Z