scholarly journals On the eigenvalues of certain canonical higher-order ordinary differential operators

2006 ◽  
Vol 322 (2) ◽  
pp. 990-1000 ◽  
Author(s):  
Albrecht Böttcher ◽  
Harold Widom
Keyword(s):  
Differential Operators ◽  
Higher Order ◽  
Ordinary Differential Operators

On the trace formula for higher-order ordinary differential operators

2021 ◽  
Vol 212 (5) ◽  
Author(s):  
Egor Denisovich Gal'kovskii ◽  
Alexander Il'ich Nazarov
Keyword(s):  
Trace Formula ◽  
Differential Operators ◽  
Higher Order ◽  
Ordinary Differential Operators

scholarly journals The variational theory of higher-order linear differential equations

1984 ◽  
Vol 95 ◽  
pp. 137-161 ◽  
Author(s):  
Yasuo Teranishi
Keyword(s):  
Differential Equations ◽  
Compact Riemann Surface ◽  
Differential Operators ◽  
Higher Order ◽  
Variational Theory ◽  
Open Set ◽  
Ordinary Differential Operators ◽  
Linear Differential ◽  
Higher Order Differential Equations ◽  
Projective Coordinate

In his paper [2], [3], D. A. Hejhal investigated the variational theory of linear polynomic functions. In this paper we are concerned with the variational theory of higher-order differential equations. To be more precise, consider a compact Riemann surface having genus g > 1. As is well known, we can choose a projective coordinate covering U = (Ua, za). Fix this coordinate covering of X. We shall be concerned with linear ordinary differential operators of order n defined in each projective coordinate open set Ua

scholarly journals Lieb–Thirring inequalities for higher order differential operators

2008 ◽  
Vol 281 (2) ◽  
pp. 199-213 ◽  
Author(s):  
Clemens Förster ◽  
Jörgen Östensson
Keyword(s):  
Differential Operators ◽  
Higher Order

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.

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