Results 261 to 270 of about 238,932 (290)

On a perturbation approach to open mapping theorems

Optimization Methods and Software, 2009
The open covering property, also known in the literature as metric regularity, is investigated for certain classes of set-valued maps in a Banach space setting. The focus of the present study is on a perturbation approach for deriving open covering criteria, which stems from a theorem due to Milyutin, and which is developed here by means of an abstract
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A note on Aupetit's perturbation theorem

Quaestiones Mathematicae, 2020
We investigate the different forms of Aupetit's perturbation theorem and its variants, and provide some generalisations.Key words: Spectrum, inessential ideal, Riesz and strong Riesz properties.
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Perturbation theorems for a-times integrated semigroups

Archiv der Mathematik, 2003
Under relative smallness conditions for the perturbing operator \(B\), perturbation results are proved for the generator \((A,D(A))\) of an \(\alpha\)-times integrated semigroup on a Banach space \(X\). More precisely, it is shown that if the estimate \[ \| B(\lambda-A)^{-1}\| \leq M\alpha+1\) if the \(\alpha\)-times integrated semigroup generated by \(
Kaiser, Cornelia, Weis, Lutz
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Perturbation Theorems for Relative Spectral Problems

Canadian Journal of Mathematics, 1972
Eigenvalue problems of the form Af = λBf, where λ is a complex parameter and A and B are operators on a Hilbert Space, have been considered by a number of authors (e.g., [1; 3; 5; 7; 10]). In this paper, we shall be concerned with the existence and nature of eigenfunction expansions associated with such problems, with no assumptions of self-adjointness.
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A perturbation theorem for exponential dichotomies

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1987
SynopsisSuppose the linear equation x' = A(t)x has an exponential dichotomy and suppose B(t) is close to A(t) in the following sense: on any interval of length 2T, B(t) is close to some translate A(t + τ) of A(t) (actually the conditions in the paper are slightly weaker than this).
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Some theorems on perturbation theory

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1949
Abstract It is proved that the well-known formulae which give the variation in the eigenvalues and eigenfunctions arising from a differential equation Φ (x) + {λ — q(x)} Φ(x) = 0, when q(x) is varied, are valid under certain general conditions. The analysis is extended to partial differential equations.
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Perturbation theorems for maximal \(L_p\)-regularity

2001
The authors consider perturbation theorems for \(R\)-sectorial operators. Let \(A\) be an \(R\)-sectorial operator in a Banach space \(X\). Let \(B\) be a perturbation for \(A\) which is relatively small with respect to \(A\). Then \(A+B\) is also \(R\)-sectorial. This result seems to be a generalization of the Kato-Rellich Theorem and the KLMN-Theorem.
Kunstmann, Peer Christian, Weis, Lutz
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Linked-diagram theorem in many-body perturbation theory

Annals of Physics, 2020
Kazuo Takayanagi
exaly  

Weyl's type theorems and perturbations

2007
Summary: Weyl's theorem for a bounded linear operator \(T\) on complex Banach spaces, as well as its variants, a-Weyl's theorem and property (w), in general is not transmitted to a perturbation \(T + K\), even when \(K\) is a ``good'' operator, such as a commuting finite rank operator or a compact operator.
AIENA, Pietro, GUILLEN J, PENA P.
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Extended Koopmans' theorem at the second‐order perturbation theory

Journal of Computational Chemistry, 2020
Xin Xu
exaly