scholarly journals Spectral Inclusions for Quasi-Fredholm and Saphar Spectra for Integrated Semigroups

2019 ◽  
Vol 53 (1) ◽  
pp. 73-85
Author(s):  
Hamid Boua ◽  
Mohammed Karmouni ◽  
Abdelaziz Tajmouati
Keyword(s):  
Integrated Semigroups ◽  
Spectral Inclusion

In this paper, we show a spectral inclusion of integrated semigroups for Saphar, essentially Saphar and quasi-Fredholm spectra.

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

scholarly journals Integrated semigroups

1989 ◽  
Vol 84 (1) ◽  
pp. 160-180 ◽  
Author(s):  
Hermann Kellerman ◽  
Matthias Hieber
Keyword(s):  
Integrated Semigroups

Integrated semigroups and integrodifferential equations

1994 ◽  
Vol 48 (1) ◽  
pp. 79-95 ◽  
Author(s):  
Ronald Grimmer ◽  
James H. Liu
Keyword(s):  
Integrodifferential Equations ◽  
Integrated Semigroups

scholarly journals Integrated cosine functions

1996 ◽  
Vol 19 (3) ◽  
pp. 575-580 ◽  
Author(s):  
Quan Zheng
Keyword(s):  
Banach Space ◽  
Cauchy Problem ◽  
Second Order ◽  
Basic Theory ◽  
Cosine Function ◽  
Integrated Semigroups ◽  
Approximation Theorems ◽  
The Relationship ◽  
Cosine Functions

In order to the second order Cauchy problem(CP2):x″(t)=Ax(t),x(0)=x∈D(An),x″(0)=y∈D(Am)on a Banach space, Arendt and Kellermann recently introduced the integrated cosine function. This paper is concerned with its basic theory, which contain some properties, perturbation and approximation theorems, the relationship to analytic integrated semigroups, interpolation and extrapolation theorems.

scholarly journals Integrated Semigroups on Fréchet Spaces I: Bochner Integral, Laplace Integral and Real Representation Theorems

2019 ◽  
Vol 11 (1) ◽  
pp. 118
Author(s):  
Tiziano Granucci
Keyword(s):  
Functional Space ◽  
Fréchet Spaces ◽  
Bochner Integral ◽  
Representation Theorems ◽  
Real Representation ◽  
Integrated Semigroups ◽  
Laplace Integral ◽  
Vectorial Functions

In this articles we will study the integration of the vectorial functions in Fréchet spaces. Particularly we will introduce and we will study a new functional space and we will prove some theorems of representation.

scholarly journals Local Integrated Semigroups: Evolution with Jumps of Regularity

1994 ◽  
Vol 186 (2) ◽  
pp. 572-595 ◽  
Author(s):  
W. Arendt ◽  
O. Elmennaoui ◽  
V. Keyantuo
Keyword(s):  
Integrated Semigroups
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