Some properties of the eigenfunctions and associated functions of an ordinary differential operator of fourth order

1986 ◽  
Vol 40 (5) ◽  
pp. 847-854
Author(s):  
N. B. Kerimov
Keyword(s):  
Differential Operator ◽  
Fourth Order ◽  
Ordinary Differential Operator ◽  
Associated Functions ◽  
Eigenfunctions And Associated Functions

scholarly journals Basis Properties of Eigenfunctions of Second-Order Differential Operators with Involution

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Asylzat Kopzhassarova ◽  
Abdizhakhan Sarsenbi
Keyword(s):  
Differential Operator ◽  
Differential Operators ◽  
Second Order ◽  
Ordinary Differential Operator ◽  
Spectral Problems ◽  
Associated Functions ◽  
Eigenfunctions And Associated Functions

We study the basis properties of systems of eigenfunctions and associated functions for one kind of generalized spectral problems for a second-order ordinary differential operator.

scholarly journals On Singular Dissipative Fourth-Order Differential Operator in Lim-4 Case

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Ekin Uğurlu ◽  
Elgiz Bairamov
Keyword(s):  
Spectral Analysis ◽  
Differential Operator ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Inverse Operator ◽  
Order Differential Operator ◽  
Associated Functions ◽  
Fourth Order Differential Operator

A singular dissipative fourth-order differential operator in lim-4 case is considered. To investigate the spectral analysis of this operator, it is passed to the inverse operator with the help of Everitt's method. Finally, using Lidskiĭ's theorem, it is proved that the system of all eigen- and associated functions of this operator (also the boundary value problem) is complete.

A class of symmetric ordinary differential operators whose deficiency numbers differ by an integer†

1978 ◽  
Vol 82 (1-2) ◽  
pp. 117-134 ◽  
Author(s):  
Richard C. Gilbert
Keyword(s):  
Differential Operator ◽  
Positive Integer ◽  
Asymptotic Expansions ◽  
Differential Operators ◽  
Ordinary Differential Operator ◽  
Ordinary Differential Operators ◽  
Half Axis ◽  
Complex Coefficients

SynopsisFormulas are determined for the deficiency numbers of a formally symmetric ordinary differential operator with complex coefficients which have asymptotic expansions of a prescribed type on a half-axis. An implication of these formulas is that for any given positive integer there exists a formally symmetric ordinary differential operator whose deficiency numbers differ by that positive integer.

scholarly journals On Stability of Basis Property of Root Vectors System of the Sturm-Liouville Operator with an Integral Perturbation of Conditions in Nonstrongly Regular Samarskii-Ionkin Type Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
N. S. Imanbaev
Keyword(s):  
Boundary Conditions ◽  
Liouville Operator ◽  
Basis Property ◽  
Differentiation Operator ◽  
Stability And Instability ◽  
Associated Functions ◽  
Sturm Liouville ◽  
Type Boundary ◽  
Eigenfunctions And Associated Functions ◽  
Integral Perturbation

We study a question on stability and instability of basis property of system of eigenfunctions and associated functions of the double differentiation operator with an integral perturbation of Samarskii-Ionkin type boundary conditions.

scholarly journals Spectral Curve of the Halphen Operator

2016 ◽  
Vol 60 (2) ◽  
pp. 451-460
Author(s):  
Andrey E. Mironov ◽  
Dafeng Zuo
Keyword(s):  
Differential Operator ◽  
Spectral Curve ◽  
Ordinary Differential Operator ◽  
Order Operator ◽  
Third Order ◽  
Image Position

AbstractThe Halphen operator is a third-order operator of the formwhere g ≠ 2 mod(3), where the Weierstrass ℘-function satisfies the equationIn the equianharmonic case, i.e. g2 = 0, the Halphen operator commutes with some ordinary differential operator Ln of order n ≠ 0 mod(3). In this paper we find the spectral curve of the pair L3, Ln.

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