scholarly journals Spectral properties of ordinary differential operators generated by first order systems

2021 ◽  
Author(s):  
А Шкаликов
Keyword(s):  
Spectral Properties ◽  
Differential Operators ◽  
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.

V.— On the Spectrum of Second Order Partial Differential Operators.

1970 ◽  
Vol 69 (1) ◽  
pp. 77-84
Author(s):  
K. J. Brown ◽  
I. M. Michael
Keyword(s):  
Differential Equations ◽  
Spectral Properties ◽  
Differential Operators ◽  
Second Order ◽  
Partial Differential ◽  
Partial Differential Operators ◽  
Ordinary Differential Operators

SynopsisIn a recent paper, Jyoti Chaudhuri and W. N. Everitt linked the spectral properties of certain second order ordinary differential operators with the analytic properties of the solutions of the corresponding differential equations. This paper considers similar properties of the spectrum of the corresponding partial differential operators.

Pencils of differential operators containing the eigenvalue parameter in the boundary conditions

2003 ◽  
Vol 133 (4) ◽  
pp. 893-917 ◽  
Author(s):  
Marco Marletta ◽  
Andrei Shkalikov ◽  
Christiane Tretter
Keyword(s):  
Boundary Conditions ◽  
Spectral Properties ◽  
Differential Operators ◽  
Finite Interval ◽  
Linear Operators ◽  
Riesz Bases ◽  
Ordinary Differential Operators ◽  
Associated Functions ◽  
Eigenvalue Parameter

The paper deals with linear pencils N − λP of ordinary differential operators on a finite interval with λ-dependent boundary conditions. Three different problems of this form arising in elasticity and hydrodynamics are considered. So-called linearization pairs (W, T) are constructed for the problems in question. More precisely, functional spaces W densely embedded in L2 and linear operators T acting in W are constructed such that the eigenvalues and the eigen- and associated functions of T coincide with those of the original problems. The spectral properties of the linearized operators T are studied. In particular, it is proved that the eigen- and associated functions of all linearizations (and hence of the corresponding original problems) form Riesz bases in the spaces W and in other spaces which are obtained by interpolation between D(T) and W.

Spectral properties of ordinary differential operators with involuton

2019 ◽  
Vol 484 (1) ◽  
pp. 12-17 ◽  
Author(s):  
V. E. Vladykina ◽  
A. A. Shkalikov
Keyword(s):  
Boundary Conditions ◽  
Unconditional Basis ◽  
Spectral Properties ◽  
Differential Operators ◽  
Root Functions ◽  
Ordinary Differential Operators ◽  
Normal Boundary ◽  
The Space L2

Let P and Q be ordinary differential operators of order n and m generated by s = max{n; m} boundary conditions on a nite interval [a; b]. We study operators of the form L = JP + Q, where J is the involution operator in the space L2[a; b]. We consider three cases n > m, n < m, and n = m, for which we dene concepts of regular, almost regular, and normal boundary conditions. We announce theorems on unconditional basis and completeness of the root functions of operator L depending on the type of boundary conditions from selected classes.

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