نتایج جستجو برای: resolvent operator

تعداد نتایج: 95455  

Journal: :Journal of Physics: Conference Series 2015

2014
YA-NING LI HONG-RUI SUN

As an extension of the fact that a sectorial operator can determine an analytic semigroup, we first show that a sectorial operator can determine a real analytic α-order fractional resolvent which is defined in terms of MittagLeffler function and the curve integral. Then we give some properties of real analytic α-order fractional resolvent. Finally, based on these properties, we discuss the regu...

2014
Zhenbin Fan Gisèle Mophou Sotiris Ntouyas

We discuss the continuity of analytic resolvent in the uniform operator topology and then obtain the compactness of Cauchy operator by means of the analytic resolvent method. Based on this result, we derive the existence of mild solutions for nonlocal fractional differential equations when the nonlocal item is assumed to be Lipschitz continuous and neither Lipschitz nor compact, respectively. A...

2007
VLADIMIR MÜLLER MICHAEL M. NEUMANN

Given a Banach space operator with interior points in the localizable spectrum and without non-trivial divisible subspaces, this article centers around the construction of an infinite-dimensional linear subspace of vectors at which the local resolvent function of the operator is bounded and even admits a continuous extension to the closure of its natural domain. As a consequence, it is shown th...

2013
Junmin Chen Xian Wang Zhen He Juhe Sun Liwei Zhang Xiantao Xiao

In this paper, a new monotonicity, M(·, ·)-monotonicity,is introduced in Banach spaces, and the resolvent operator of an M(·, ·)monotone operator is proved to be single valued and Lipschitz continuous. By using the resolvent operator technique associated with M(·, ·)monotone operators, we construct a proximal point algorithm for solving a class of variational inclusions. And we prove the conver...

2017
M. BURAK ERDOĞAN MICHAEL GOLDBERG WILLIAM R. GREEN

In this paper we consider Dirac operators in R, n ≥ 2, with a potential V . Under mild decay and continuity assumptions on V and some spectral assumptions on the operator, we prove a limiting absorption principle for the resolvent, which implies a family of Strichartz estimates for the linear Dirac equation. For large potentials the dynamical estimates are not an immediate corollary of the free...

2007
Vladimı́r Müller

We exhibit an example of a bounded linear operator on a Banach space which admits an everywhere defined local resolvent with continuous derivatives of all orders. Let T be a bounded linear operator acting on a complex Banach space X. It is well known that the resolvent z 7→ (T − z)−1 defined on the complement of the spectrum σ(T ) is unbounded. More precisely, ‖(T − z)−1‖ → ∞ whenever z approac...

2012
Simona Macovei S. Macovei

Having as start point the classic definitions of resolvent set and spectrum of a linear bounded operator on a Banach space, we introduce the resolvent set and spectrum of a family of linear bounded operators on a Banach space. In addition, we present some results which adapt to asymptotic case the classic results.

2002
N. CASTRO GONZÁLEZ J. J. KOLIHA

In this paper, we investigate a perturbation of the Drazin inverse AD of a closed linear operator A; the main tool for obtaining the estimates is the gap between subspaces and operators. By (X) we denote the set of all closed linear operators acting on a linear subspace of X to X , where X is a complex Banach space. We write (A), (A), (A), ρ(A), σ(A), and R(λ,A) for the domain, nullspace, range...

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