Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

The Spectral Analysis of a Nuclear Resolvent Operator Associated with a Second Order Dissipative Differential Operator

The Spectral Analysis of a Nuclear Resolvent Operator Associated with a Second Order Dissipative... In this paper, we introduce a new approach for the spectral analysis of a linear second order dissipative differential operator with distributional potentials. This approach is related with the inverse operator. We show that the inverse operator is a non-selfadjoint trace class operator. Using Lidskiĭ’s theorem, we introduce a complete spectral analysis of the second order dissipative differential operator. Moreover, we give a trace formula for the trace class integral operator. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

The Spectral Analysis of a Nuclear Resolvent Operator Associated with a Second Order Dissipative Differential Operator

Download PDF
17 pages

Loading next page...
 
/lp/springer-journals/the-spectral-analysis-of-a-nuclear-resolvent-operator-associated-with-V9GrFdtr0P
Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-016-0185-8
Publisher site
See Article on Publisher Site

Abstract

In this paper, we introduce a new approach for the spectral analysis of a linear second order dissipative differential operator with distributional potentials. This approach is related with the inverse operator. We show that the inverse operator is a non-selfadjoint trace class operator. Using Lidskiĭ’s theorem, we introduce a complete spectral analysis of the second order dissipative differential operator. Moreover, we give a trace formula for the trace class integral operator.

Journal

Computational Methods and Function Theory – Springer Journals

Published: Oct 31, 2016

References

  • Inequalities between the two kinds of eigenvalues of a linear transformation
    Weyl, H
  • 485–487 (in Russian)
    Lidskiĭ, VB
  • Functional analysis
    Lax, P
  • Linear operators part II: spectral theory
    Dunford, N; Schwartz, JT
  • On spectral decomposition of linear non-self-adjoint operators
    Livšic, MS
  • Recent developments in some non-self-adjoint problems of mathematical physics
    Dolph, CL
  • Sturm-Liouville operators with singular potentials
    Savchuk, AM; Shkalikov, AA
  • Weyl-Titchmarsh theory for Sturm-Liouville operators with distributional potentials
    Eckhardt, J; Gesztesy, F; Nichols, R; Teschl, G
  • Sturm-Liouville theory, mathematical surveys and monographs, 121
    Zettl, A
  • Discrete and continuous boundary problems
    Atkinson, FV
  • On the deficiency indices and selfadjointness of symmetric Hamiltonian system
    Lesch, M; Malamud, M
  • Limit point and limit circle classification for sympletic systems on time scales
    Hilscher, RS; Zemánek, P
  • Spectral analysis of dissipative Schrodinger operators
    Allahverdiev, BP; Canoglu, A
  • Dissipative operators generated by the Sturm-Liouville expression in the Weyl limit circle case
    Bairamov, E; Krall, AM
  • Eigenparameter dependent Sturm-Liouville problems in boundary conditions with transmission conditions
    Allahverdiev, BP; Bairamov, E; Ugurlu, E
  • Spectral analysis of eigenparameter dependent boundary value transmission problems
    Uğurlu, E; Bairamov, E
  • The determinants of dissipative Sturm-Liouville operators with transmission conditions
    Bairamov, E; Ugurlu, E
  • Krein’s theorem for the dissipative operators with finite impulsive effects
    Uğurlu, E; Bairamov, E
  • On the indeterminate case of the Sturm-Liouville boundary problem in the interval $$(0,\infty )$$ ( 0 , ∞ )
    Krein, MG
  • On the nuclearity of integral operators
    Ferreira, JC; Menegatto, VA; Oliveira, CP