A trace formula for integro-differential operators on the finite interval

2017 ◽  
Vol 33 (1) ◽  
pp. 141-146
Author(s):  
Yu-ping Wang ◽  
Hikmet Koyunbakan ◽  
Chuan-fu Yang
Keyword(s):  
Trace Formula ◽  
Differential Operators ◽  
Finite Interval

The Spectrum and Trace Formula for Bounded Perturbations of Differential Operators

2018 ◽  
Vol 98 (3) ◽  
pp. 552-554
Author(s):  
V. A. Sadovnichy ◽  
Z. Yu. Fazullin ◽  
I. G. Nugaeva
Keyword(s):  
Trace Formula ◽  
Differential Operators ◽  
Bounded Perturbations

The Spectrum and the Trace Formula for Bounded Perturbations of Differential Operators

2018 ◽  
Vol 483 (1) ◽  
pp. 19-21
Author(s):  
V. Sadovnichy ◽  
◽  
Z. Fazullin ◽  
I. Nugaeva ◽  
◽  
...  
Keyword(s):  
Trace Formula ◽  
Differential Operators ◽  
Bounded Perturbations

scholarly journals Spectrums of Solvable Pantograph Differential-Operators for First Order

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Z. I. Ismailov ◽  
P. Ipek
Keyword(s):  
Hilbert Space ◽  
Differential Operator ◽  
Operator Theory ◽  
Differential Operators ◽  
Finite Interval ◽  
Exact Formula ◽  
Operator Expression ◽  
Minimal Operator ◽  
First Order ◽  
Delay Differential

By using the methods of operator theory, all solvable extensions of minimal operator generated by first order pantograph-type delay differential-operator expression in the Hilbert space of vector-functions on finite interval have been considered. As a result, the exact formula for the spectrums of these extensions is presented. Applications of obtained results to the concrete models are illustrated.

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.

On the trace formula for higher-order ordinary differential operators

2021 ◽  
Vol 212 (5) ◽  
Author(s):  
Egor Denisovich Gal'kovskii ◽  
Alexander Il'ich Nazarov
Keyword(s):  
Trace Formula ◽  
Differential Operators ◽  
Higher Order ◽  
Ordinary Differential Operators

Trace formula for nonlocal differential operators

2019 ◽  
Vol 50 (4) ◽  
pp. 1107-1114 ◽  
Author(s):  
Xin-Jian Xu ◽  
Chuan-Fu Yang
Keyword(s):  
Trace Formula ◽  
Differential Operators

TRACE FORMULA FOR GREEN'S FUNCTIONS OF EFFECTIVE MASS SCHRÖDINGER EQUATIONS AND NTH-ORDER DARBOUX TRANSFORMATIONS

2008 ◽  
Vol 23 (16n17) ◽  
pp. 2635-2647 ◽  
Author(s):  
EKATERINA POZDEEVA ◽  
AXEL SCHULZE-HALBERG
Keyword(s):  
Effective Mass ◽  
Trace Formula ◽  
Green's Functions ◽  
Arbitrary Order ◽  
Finite Interval ◽  
Green’S Functions ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Darboux Transformations ◽  
Mass Case

We derive a trace formula for Green's functions of position-dependent (effective) mass Schrödinger equations that are defined on a real, finite interval and connected by a Darboux transformation of arbitrary order. Our findings generalize former results (J. Phys. A37, 10287 (2004)) on constant mass Schrödinger equations to the effective mass case.

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