On the basis property of Riesz means of spectral expansions corresponding to a nonself-adjoint ordinary differential operator of higher order: I

2000 ◽  
Vol 36 (3) ◽  
pp. 337-348
Author(s):  
A. M. Zuev
Keyword(s):  
Differential Operator ◽  
Basis Property ◽  
Higher Order ◽  
Ordinary Differential Operator ◽  
Riesz Means ◽  
Spectral Expansions

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.

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.

The Expansion Theorems for Sturm-Liouville Operators with an Involution Perturbation

2021 ◽  
Author(s):  
Abdizhahan Sarsenbi
Keyword(s):  
Differential Operator ◽  
Differential Operators ◽  
Second Order ◽  
Order Differential Operator ◽  
Spectral Expansions ◽  
Sturm Liouville ◽  
Complex Valued ◽  
Liouville Operators

In this work, we studied the Green’s functions of the second order differential operators with involution. Uniform equiconvergence of spectral expansions related to the second-order differential operators with involution is obtained. Basicity of eigenfunctions of the second-order differential operator operator with complex-valued coefficient is established.

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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