scholarly journals Commuting ordinary differential operators of arbitrary genus and arbitrary rank with polynomial coefficients

2014 ◽  
pp. 323-336 ◽  
Author(s):  
O. I. Mokhov
Keyword(s):  
Differential Operators ◽  
Arbitrary Rank ◽  
Polynomial Coefficients ◽  
Ordinary Differential Operators ◽  
Arbitrary Genus

scholarly journals SOME RESULTS ON ESSENTIAL SPECTRA OF DIFFERENTIAL OPERATORS IN BANACH SPACES

2003 ◽  
Vol 8 (3) ◽  
pp. 203-216
Author(s):  
V. A. Erovenko
Keyword(s):  
Banach Spaces ◽  
Differential Operators ◽  
Lebesgue Spaces ◽  
Essential Spectra ◽  
Polynomial Coefficients ◽  
Ordinary Differential Operators

In this paper we investigate spectral and semi‐Predholm properties of maximum and minimum Puchsian differential operators on Lebesgue spaces on a semi‐axis. These results are applied for determination of various essential spectra and spectrum of ordinary differential operators with polynomial coefficients, which order does not exceed the order of the corresponding derivative.

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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