HOCHSTADT-LIEBERMAN TYPE THEOREM FOR A NON-SYMMETRIC SYSTEM OF FIRST-ORDER ORDINARY DIFFERENTIAL OPERATORS

2003 ◽  
Author(s):  
IGOR TROOSHIN ◽  
MASAHIRO YAMAMOTO
Keyword(s):  
Differential Operators ◽  
Type Theorem ◽  
Symmetric System ◽  
First Order ◽  
Ordinary Differential Operators

scholarly journals Spectral properties of first order ordinary differential operators with short range potentials

1980 ◽  
Vol 79 ◽  
pp. 23-32
Author(s):  
S. Itatsu ◽  
H. Kaneta
Keyword(s):  
Spectral Properties ◽  
Short Range ◽  
Differential Operators ◽  
Hermitian Matrix ◽  
Constant Matrix ◽  
Complete Proof ◽  
First Order ◽  
Ordinary Differential Operators

The purpose of the present paper is to give a complete proof of the theorem which will be used in a paper of the second author [4].We will discuss certain spectral properties of selfadjoint ordinary differential operators of the form iA(d/dx) + V acting in L2(R)n = Σ ⊕ L2(R)n, where A is a real diagonal constant matrix and V an Hermitian matrix valued function on R which satisfies some conditions to be stated in the sequel.

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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