共查询到10条相似文献,搜索用时 109 毫秒
1.
Noboru Okazawa 《Integral Equations and Operator Theory》2000,38(4):458-500
The imaginary powersA
it of a closed linear operatorA, with inverse, in a Banach spaceX are considered as aC
0-group {exp(itlogA);t R} of bounded linear operators onX, with generatori logA. Here logA is defined as the closure of log(1+A) – log(1+A
–1). LetA be a linearm-sectorial operator of typeS(tan ), 0(/2), in a Hilbert spaceX. That is, |Im(Au, u)| (tan )Re(Au, u) foru D(A). Then ±ilog(1+A) ism-accretive inX andilog(1+A) is the generator of aC
0-group {(1+A)
it
;t R} of bounded imaginary powers, satisfying the estimate (1+A)
it
exp(|t|),t R. In particular, ifA is invertible, then ±ilogA ism-accretive inX, where logA is exactly given by logA=log(1+A)–log(1+A
–1), and {A
it;t R} forms aC
0-group onX, with the estimate A
it exp(|t|),t R. This yields a slight improvement of the Heinz-Kato inequality. 相似文献
2.
The sign portrait S of a real n× n matrix is a matrix over the semiring with elements 0, 1, -1, and , where symbolizes indeterminateness. It is proved that if k is the least positive integer such that all the entries of S
k are equal to , then k 2n
2 – 3n + 2, and this bound is sharp. Bibliography: 6 titles. 相似文献
3.
The hypermetric coneH
n is the cone in the spaceR
n(n–1)/2 of all vectorsd=(d
ij)1i<jn
satisfying the hypermetric inequalities: –1ijn
z
j
z
j
d
ij
0 for all integer vectorsz inZ
n with –1in
z
i
=1. We explore connections of the hypermetric cone with quadratic forms and the geometry of numbers (empty spheres andL-polytopes in lattices). As an application, we show that the hypermetric coneH
n is polyhedral. 相似文献
4.
LetX be a complex Banach space andA: D(A)X a densely defined closed linear operator whose resolvent set contains the real line and for which (–A)–1 is bounded onR. We give a necessary and sufficient condition, in terms of the complex powers ofA and –A, for the existence of a decompositionX=X
+X
–, whereX
± are closed subspaces, invariant forA, the spectra of the reduced operatorsA
± are {(A);Im>0} and {(A);Im<0} respectively, and (–A
±)–1 is bounded forIm0.Finally we give an example of an operator in anL
p-type space for which the decomposition exists if 1<p<+ and does not exist ifp=1. 相似文献
5.
We consider a 2-periodic function f continuous on
and changing its sign at 2s points y
i [–, ). For this function, we prove the existence of a trigonometric polynomial T
n of degree n that changes its sign at the same points y
i and is such that the deviation |f(x) – T
n(x)| satisfies the second Jackson inequality. 相似文献
6.
For a graphG, letp(G) andc(G) denote the length of a longest path and cycle, respectively. Let (t,n) be the minimum ofp(G), whereG ranges over allt-tough connected graphs onn vertices. Similarly, let (t,n) be the minimum ofc(G), whereG ranges over allt-tough 2-connected graphs onn vertices. It is shown that for fixedt>0 there exist constantsA, B such that (t,n)A·log(n) and (t,n)·log((t,n))B·log(n). Examples are presented showing that fort1 there exist constantsA, B such that (t,n)A·log(n) and (t,n)B· log(n). It is conjectured that (t,n) B·log(n) for some constantB. This conjecture is shown to be valid within the class of 3-connected graphs and, as conjectured in Bondy [1] forl=3, within the class of 2-connectedK
1.l-free graphs, wherel is fixed. 相似文献
7.
LetA be a subset of a balayage space (X,W) and a measure onX. It is shown that for every sequence n of measures such that limnn and limn
n
A
= the limit measure is of the formf+[(1-f)]A for some (unique) Borel function 0f1Cb(A). Furthermore, conditions are given such that any such functionf occurs. 相似文献
8.
In this paper we obtain estimates which are order-exact for the projection and Macphail constants of an arbitrary n-dimensional Banach space: 1(X)n, 1/n1(X)1/n.Translated from Matematicheskii Zametki, Vol. 10, No. 4, pp. 453–457, 1971. 相似文献
9.
A sign pattern matrix is a matrix whose entries are from the set {+,–,0}. The purpose of this paper is to obtain bounds on the minimum rank of any symmetric sign pattern matrix A whose graph is a tree T (possibly with loops). In the special case when A is nonnegative with positive diagonal and the graph of A is star-like, the exact value of the minimum rank of A is obtained. As a result, it is shown that the gap between the symmetric minimal and maximal ranks can be arbitrarily large for a symmetric tree sign pattern A.
Supported by NSF grant No. DMS-00700AMS classification: 05C50, 05C05, 15A48 相似文献
10.
S. R. Treil' 《Journal of Mathematical Sciences》1989,44(6):868-869
It is proved that for every sequence of points n from the unit circle, n1, and for an arbitrary sequence of positive numbers An, An, there exists a continuous real function u, such that for the Toeplitz operator T (acting in the Hardy space H2) with the symbol =e
iu
we have the estimates (T–nI)–1>An, n.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, AN SSSR, Vol. 157, pp. 175–177, 1987. 相似文献