scholarly journals ESSENTIAL SPECTRA OF ORDINARY DIFFERENTIAL OPERATORS II. STABILITY OF SPECTRA

2020 ◽  
pp. 7-13
Author(s):  
V. A. Erovenko
Keyword(s):  
Differential Operators ◽  
Classical Theorem ◽  
Lebesgue Spaces ◽  
Essential Spectra ◽  
Ordinary Differential Operators

The article contains precise formulas for finding of the essential spectra that are revolted with asymptotically constants on infinity in coefficients with use of rather compact and rather small indignations on infinity in Lebesgue spaces of 𝐿 𝑝 . These formulas are new analogs of the classical theorem of Weyl.

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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