On an analog of the Riesz theorem and the basis property of the system of root functions of a differential operator in Lp: II

被引：0

作者：

V. M. Kurbanov

机构：

[1] National Academy of Sciences,Institute for Mathematics and Mechanics

来源：

Differential Equations | 2013年 / 49卷

关键词：

Differential Equation; Basis Property; Compact Operator; Root Function; Eigenfunction Expansion;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We consider an ordinary differential operator of arbitrary order, obtain necessary conditions for the Riesz property of systems of normalized root functions, prove an analog of the Riesz theorem, and use it to obtain sufficient conditions for the basis property of the system of root functions of the given operator in Lp.

引用

页码：437 / 449

页数：12

共 50 条

[31] The Bessel property and the unconditional basis property of systems of root vector functions of the Dirac operator
Kurbanov, VM
[J]. DIFFERENTIAL EQUATIONS, 1996, 32 (12) : 1601 - 1610
[32] Basis property of root functions of second order differential operators
Lomov, IS
[J]. DOKLADY AKADEMII NAUK, 1997, 356 (05) : 595 - 598
[33] ON THE REGULARITY AND THE RIESZ BASIS PROPERTY OF SCALING FUNCTIONS
HERVE, L
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1992, 315 (10): : 1029 - 1032
[34] On the basis property of the root functions of differential operators with matrix coefficients
Veliev, Oktay A.
[J]. CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2011, 9 (03): : 657 - 672
[35] Riesz bases formed by root functions of a functional-differential equation with a reflection operator
V. P. Kurdyumov
A. P. Khromov
[J]. Differential Equations, 2008, 44 : 203 - 212
[36] Riesz bases formed by root functions of a functional-differential equation with a reflection operator
Kurdyumov, V. P.
Khromov, A. P.
[J]. DIFFERENTIAL EQUATIONS, 2008, 44 (02) : 203 - 212
[37] ON RIESZ BASIS OF SYSTEMS OF EIGEN-FUNCTIONS AND ASSOCIATED FUNCTIONS OF DIFFERENTIAL-EQUATIONS WITH OPERATOR COEFFICIENTS
RAKHIMOV, M
[J]. DOKLADY AKADEMII NAUK SSSR, 1987, 293 (03): : 538 - 540
[38] On the basis property of Riesz means of spectral expansions corresponding to a nonself-adjoint ordinary differential operator of higher order: II
A. M. Zuev
[J]. Differential Equations, 2000, 36 : 504 - 510
[39] On the basis property of Riesz means of spectral expansions corresponding to a nonself-adjoint ordinary differential operator of higher order: II
Zuev, AM
[J]. DIFFERENTIAL EQUATIONS, 2000, 36 (04) : 504 - 510
[40] Stability of the basis property of system of root functions of Sturm-Liouville operator with integral boundary condition
Imanbaev, Nurlan
[J]. APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'16), 2016, 1789

← 1 2 3 4 5 →