scholarly journals Spectral inclusion and pollution for a class of dissipative perturbations

2021 ◽  
Vol 62 (1) ◽  
pp. 013501
Author(s):  
Alexei Stepanenko
Keyword(s):  
Spectral Inclusion

scholarly journals Regular approximation of singular Sturm–Liouville problems with eigenparameter dependent boundary conditions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Maozhu Zhang ◽  
Kun Li ◽  
Hongxiang Song
Keyword(s):  
Boundary Conditions ◽  
Operator Theory ◽  
Resolvent Convergence ◽  
Spectral Inclusion ◽  
Regular Approximation ◽  
Special Cases ◽  
Abstract Operator ◽  
Norm Resolvent Convergence ◽  
Sturm Liouville ◽  
Spectral Exactness

AbstractIn this paper we consider singular Sturm–Liouville problems with eigenparameter dependent boundary conditions and two singular endpoints. The spectrum of such problems can be approximated by those of the inherited restriction operators constructed. Via the abstract operator theory, the strongly resolvent convergence and norm resolvent convergence of a sequence of operators are obtained and it follows that the spectral inclusion of spectrum holds. Moreover, spectral exactness of spectrum holds for two special cases.

scholarly journals Spectral Inclusion and Analytic Continuation

1999 ◽  
Vol 31 (6) ◽  
pp. 722-728 ◽  
Author(s):  
A. Atzmon ◽  
A. Eremenko ◽  
M. Sodin
Keyword(s):  
Analytic Continuation ◽  
Spectral Inclusion

Spectral Inclusion Relations for T, T | Y, and T/Y

1992 ◽  
Vol 116 (3) ◽  
pp. 763
Author(s):  
Kotaro Tanahashi ◽  
Shigeru Yamagami
Keyword(s):  
Spectral Inclusion ◽  
Inclusion Relations

scholarly journals On duality and spectral properties of (a, k)-regularized resolvents

2009 ◽  
Vol 139 (3) ◽  
pp. 505-517 ◽  
Author(s):  
Carlos Lizama ◽  
Humberto Prado
Keyword(s):  
Duality Theory ◽  
Spectral Properties ◽  
Dual Space ◽  
The Sun ◽  
Spectral Inclusion

We construct a duality theory for (a, k)-regularized resolvents, extending some of the known theorems for dual semigroups. We present several classes of spaces, which in the semigroup case correspond to the Favard class and the sun-dual space. By duality arguments spectral inclusion theorems for regularized resolvents are also obtained.

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