The Uniform Convergence of Fourier Series in a System of Polynomials Orthogonal in the Sense of Sobolev and Associated to Jacobi Polynomials

被引：1

作者：

Magomed-Kasumov, M. G. ^{[1
,2
]}

机构：

[1] Daghestan Fed Res Ctr, Makhachkala, Russia

[2] Vladikavkaz Sci Ctr, Vladikavkaz, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2023年 / 64卷 / 02期

关键词：

Sobolev inner product; Jacobi polynomials; Fourier series; uniform convergence; Sobolev space; Muckenhoupt conditions; ASYMPTOTICS;

D O I：

10.1134/S0037446623020088

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish that the Fourier series in the Sobolev system of polynomials P-alpha,P-beta (r), with -1 < alpha, beta = 0, associated to the Jacobi polynomials converge uniformly on [-1, 1] to functions in the Sobolev space W-r (L1 rho(alpha,beta)), where.(alpha,beta) is the Jacobi weight. We show also that the Fourier series converges in the norm of the Sobolev space W-r (rho)(L rho) with p > 1 under the Muckenhoupt conditions.

引用

页码：338 / 346

页数：9

共 22 条

[1] Fourier series for coherent pairs of Jacobi measures [J].

Ciaurri, Oscar ;

Minguez Ceniceros, Judit .

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2021, 32 (5-8) :437-457

[2] Fourier series of Jacobi-Sobolev polynomials [J].

Ciaurri, Oscar ;

Minguez Ceniceros, Judit .

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2019, 30 (04) :334-346

[3] Fourier Series of Gegenbauer-Sobolev Polynomials [J].

Ciaurri, Oscar ;

Minguez, Judit .

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2018, 14

[4] Discrete-Continuous Jacobi-Sobolev Spaces and Fourier Series [J].

Diaz-Gonzalez, Abel ;

Marcellan, Francisco ;

Pijeira-Cabrera, Hector ;

Urbina, Wilfredo .

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2021, 44 (02) :571-598

[5] Jacobi-Sobolev orthogonal polynomials: Asymptotics and a Cohen type inequality [J].

Fejzullahu, B. Xh. ;

Marcellan, F. ;

Moreno-Balcazar, J. J. .

JOURNAL OF APPROXIMATION THEORY, 2013, 170 :78-93

[6] Asymptotic properties and Fourier expansions of orthogonal polynomials with a non-discrete Gegenbauer-Sobolev inner product [J].

Fejzullahu, Bujar Xh .

JOURNAL OF APPROXIMATION THEORY, 2010, 162 (02) :397-406

[7]

Fejzullahu BXh, 2009, COMMUN ANALYTIC THEO, V16, P1

[8]

Fikhtengolts G. M., 2003, COURSE DIFFERENTIAL

[9] SOBOLEV-ORTHONORMAL SYSTEM OF FUNCTIONS GENERATED BY THE SYSTEM OF LAGUERRE FUNCTIONS [J].

Gadzhimirzaev, R. M. .

PROBLEMY ANALIZA-ISSUES OF ANALYSIS, 2019, 8 (01) :32-46

[10] ON POLYNOMIALS ORTHOGONAL WITH RESPECT TO CERTAIN SOBOLEV INNER PRODUCTS [J].

ISERLES, A ;

KOCH, PE ;

NORSETT, SP ;

SANZSERNA, JM .

JOURNAL OF APPROXIMATION THEORY, 1991, 65 (02) :151-175

← 1 2 3 →