scholarly journals Uniform Convergence of the Spectral Expansion for a Differential Operator with Periodic Matrix Coefficients

2008 ◽  
Vol 2008 (1) ◽  
pp. 628973 ◽  
Author(s):  
OA Veliev
Keyword(s):  
Differential Operator ◽  
Uniform Convergence ◽  
Spectral Expansion ◽  
Periodic Matrix ◽  
Matrix Coefficients

scholarly journals Absolute and Uniform Convergence of Spectral Expansion in the Eigenfunctions of a Third-Order Ordinary Differential Operator

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Differential Operator ◽  
Uniform Convergence ◽  
Sufficient Conditions ◽  
Spectral Expansion ◽  
Ordinary Differential Operator ◽  
Third Order ◽  
Spectral Expansions

In this paper studied the convergence of spectral expansions of functions of the class W1 1 ( ) G ,G= ( ) 0,1 in eigenfunctions of an ordinary differential operator of third order with integral coefficients. Sufficient conditions for absolute and uniform convergence are obtained and the rate of uniform convergence of these expansions on the interval G is found.

scholarly journals On the Differential Operators with Periodic Matrix Coefficients

2009 ◽  
Vol 2009 ◽  
pp. 1-21 ◽  
Author(s):  
O. A. Veliev
Keyword(s):  
Differential Operator ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Differential Operators ◽  
The Self ◽  
Asymptotic Formulas ◽  
Eigenvalues And Eigenfunctions ◽  
Periodic Matrix ◽  
Matrix Coefficients

We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and quasiperiodic boundary conditions. Then by using these asymptotic formulas, we find conditions on the coefficients for which the number of gaps in the spectrum of the self-adjoint differential operator with the periodic matrix coefficients is finite.

scholarly journals Absolute and uniform convergence of spectral expansion of the function from the class W1p(g), p > 1, in eigenfunctions of third order differential operator

2017 ◽  
Vol 101 (115) ◽  
pp. 169-182
Author(s):  
V.M. Kurbanov ◽  
E.B. Akhundova
Keyword(s):  
Differential Operator ◽  
Convergence Rate ◽  
Uniform Convergence ◽  
Spectral Expansion ◽  
Ordinary Differential Operator ◽  
Order Differential Operator ◽  
Third Order ◽  
Uniform Convergence Rate

We study an ordinary differential operator of third order and absolute and uniform convergence of spectral expansion of the function from the class W1p(G), G = (0,1), p > 1, in eigenfunctions of the operator. Uniform convergence rate of this expansion is estimated.

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