scholarly journals Krall–Laguerre commutative algebras of ordinary differential operators

2011 ◽  
Vol 192 (2) ◽  
pp. 203-224 ◽  
Author(s):  
Plamen Iliev
Keyword(s):  
Differential Operators ◽  
Commutative Algebras ◽  
Ordinary Differential Operators

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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