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1.
Summary In this paper we investigate the set of eigenvalues of a perturbed matrix {ie509-1} whereA is given and n × n, ||< is arbitrary. We determine a lower bound for thisspectral value set which is exact for normal matricesA with well separated eigenvalues. We also investigate the behaviour of the spectral value set under similarity transformations. The results are then applied tostability radii which measure the distance of a matrixA from the set of matrices having at least one eigenvalue in a given closed instability domain b. 相似文献
2.
Guillermo López Lagomasino 《Constructive Approximation》1989,5(1):199-219
Letd be a finite positive Borel measure on the interval [0, 2] such that >0 almost everywhere; andW
n be a sequence of polynomials, degW
n
=n, whose zeros (w
n
,1,,w
n,n
lie in [|z|1]. Let d
n
<> for eachnN, whered
n
=d/|W
n
(e
i
)|2. We consider the table of polynomials
n,m such that for each fixednN the system
n,m,mN, is orthonormal with respect tod
n
. If
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3.
Let the functionQ be holomorphic in he upper half plane + and such that ImQ(z 0 and ImzQ(z) 0 ifz +. A basic result of M.G. Krein states that these functionsQ are the principal Titchmarsh-Weyl coefficiens of a (regular or singular) stringS[L,m] with a (non-decreasing) mass distribution functionm on some interval [0,L) with a free left endpoint 0. This string corresponds to the eigenvalue problemdf +
fdm = 0; f(0–) = 0. In this note we show that the set of functionsQ which are holomorphic in + and such that the kernel
has negative squares of + and ImzQ(z) 0 ifz + is the principal Titchmarsh-Weyl coefficient of a generalized string, which is described by the eigenvalue problemdf +f
dm +
2
fdD = 0 on [0,L),f(0–) = 0. Here is the number of pointsx whereD increases or 0 >m(x + 0) –m(x – 0) –; outside of these pointsx the functionm is locally non-decreasing and the functionD is constant.To the memory of M.G. Krein with deep gratitude and affection.This author is supported by the Fonds zur Förderung der wissenschaftlichen Forschung of Austria, Project P 09832 相似文献
4.
5.
Let X be a Banach space and a strongly continuous group of linear operators on X. Set and where is the unit circle and denotes the spectrum of T(t). The main result of this paper is: is uniformly continuous if and only if is non-meager. Similar characterizations in terms of the approximate point spectrum and essential spectra are also derived.
Received: 14 June 2006, Revised: 27 September 2007 相似文献
6.
LetV
n
={1, 2, ...,n} ande
1,e
2, ...,e
N
,N=
be a random permutation ofV
n
(2). LetE
t={e
1,e
2, ...,e
t} andG
t=(V
n
,E
t
). If is a monotone graph property then the hitting time() for is defined by=()=min {t:G
t
}. Suppose now thatG
starts to deteriorate i.e. loses edges in order ofage, e
1,e
2, .... We introduce the idea of thesurvival time =() defined by t = max {u:(V
n, {e
u,e
u+1, ...,e
T
}) }. We study in particular the case where isk-connectivity. We show that
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