scholarly journals Riesz Inequality for the System of Root Functions of Second Order Ordinary Differential Operator

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Differential Operator ◽  
Sufficient Conditions ◽  
Second Order ◽  
Ordinary Differential Operator ◽  
Root Functions ◽  
Riesz Property ◽  
System Of Root Functions ◽  
The Given ◽  
Riesz Inequality

An ordinary differential operator of second order with coefficients is considered. The Riesz property of the system of root functions of the given operator is studied. The criterion of Bessel property in 2 L , of root functions system is established and use it to obtain sufficient conditions for the Riesz property of a system of normalized root functions of this operator in p L .

scholarly journals On Basis Property of Root Functions For a Class Second Order Differential Operator

2020 ◽  
Vol 5 (1) ◽  
pp. 361-368
Author(s):  
Volkan Ala ◽  
Khanlar R. Mamedov
Keyword(s):  
Differential Operator ◽  
Boundary Conditions ◽  
Spectral Parameter ◽  
Liouville Equation ◽  
Basis Property ◽  
Second Order ◽  
Order Differential Operator ◽  
Root Functions ◽  
Sturm Liouville

AbstractIn this work we investigate the completeness, minimality and basis properties of the eigenfunctions of one class discontinuous Sturm-Liouville equation with a spectral parameter in boundary conditions.

scholarly journals On Multiple Completeness of the Root Functions of Ordinary Differential Polynomial Pencil with Constant Coefficients

2017 ◽  
Vol 63 (2) ◽  
pp. 340-361
Author(s):  
V S Rykhlov
Keyword(s):  
Differential Operators ◽  
Sufficient Conditions ◽  
Differential Polynomial ◽  
Finite Segment ◽  
Root Functions ◽  
Multiple Completeness ◽  
Integrable Functions ◽  
Constant Coefficients ◽  
System Of Root Functions ◽  
Square Integrable Functions

In the space of square integrable functions on a finite segment we consider a class of polynomial pencils of nth-order ordinary differential operators with constant coefficients and two-point boundary-value conditions (at the edges of the segment). We suppose that roots of the characteristic equation of pencils of this class are simple and nonzero. We establish sufficient conditions for m-multiple completeness (1≤m≤n) of the system of root functions of pencils from this class in the space of square integrable functions on this segment.

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.

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