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1.
Let =(n)n1 be a log concave sequence such that lim infn+n/nc>0for some c>0 and ((log n)/n)n1 is nonincreasing for some<1/2. We show that, if T is a contraction on the Hilbertspace with spectrum a Carleson set, and if ||Tn||=O(n)as n tends to + with n11/(n log n)=+, then T is unitary. Onthe other hand, if n11/(n log n)<+, then there exists a (non-unitary)contraction T on the Hilbert space such that the spectrum ofT is a Carleson set, ||Tn||=O(n) as n tends to +, andlim supn+||Tn||=+. 相似文献
2.
The main result of this paper is the establishment of the fullMüntz Theorem in C[0, l]. This characterizes thesequences of distinct, positive real numbers for which span{l, x1, x2, ...} is dense in C[0,1]. The novelty of this result is the treatment of the mostdifficult case when infii = 0 while supii = . The paper settlesthe L and L1 cases of the following. THEOREM (Full Müntz Theorem in Lp[0,1]). Let p [l, ].Suppose that is a sequence of distinct real numbers greater than –1/p. Then span{x0,x1, ...} is dense in Lp[0, 1] if and only if
相似文献
3.
We investigate asymptotic behaviour of solutions of the functional-differentialequation
where f and g arelocally Lipschitz functions, C is a continuous matrix and thesmooth lag function obeys 0 (t) t for t 0. We transformthe equation into a delay equation with an infinity of delaysand use a theorem of Söderlind to derive sufficient conditionsfor stability and for asymptotic stability in the case limt (t) = . The situation is qualitatively different when limt (t) = * < and we outline stability conditions for thatcase by employing direct techniques. 相似文献
4.
Identity Theorems for Functions of Bounded Characteristic 总被引:1,自引:0,他引:1
Suppose that f(z) is a meromorphic function of bounded characteristicin the unit disk :|z|<1. Then we shall say that f(z)N. Itfollows (for example from [3, Lemma 6.7, p. 174 and the following])that
where h1(z), h2(z) are holomorphic in and have positive realpart there, while 1(z), 2(z) are Blaschke products, that is,
where p is a positive integer or zero, 0<|aj|<1, c isa constant and (1|aj|)<. We note in particular that, if c0, so that f(z)0,
(1.1) so that f(z)=0 only at the points aj. Suppose now that zj isa sequence of distinct points in such that |zj|1 as j and (1|zj|)=. (1.2) If f(zj)=0 for each j and fN, then f(z)0. N. Danikas [1] has shown that the same conclusion obtains iff(zj)0 sufficiently rapidly as j. Let j, j be sequences of positivenumbers such that j< and j as j. Danikas then defines
and proves Theorem A. 相似文献
5.
Dilworth S. J.; Ferenczi V.; Kutzarova Denka; Odell E. 《Journal London Mathematical Society》2007,75(2):409-419
Let 1 p and let X be a Banach space with a semi-normalizedstrongly asymptotic p basis (ei). If X is minimal and 1 p <2, then X is isomorphic to a subspace of p. If X is minimaland 2 p < , or if X is complementably minimal and 1 p , then (ei) is equivalent to the unit vector basis of p (orc0 if p = ). 相似文献
6.
Using Szemeredi's theorem on arithmetic progressions, it isshown that, for 1 < p < , the infinite l direct sum (Lp Lp · · · )l is a primary Banach space. 相似文献
7.
Let [ ] denote the integer part. Among other results in [3]we gave a complete solution to the following problem. PROBLEM. Given an increasing sequence an R+, n = 1, 2, ...,where an as n , are there infinitely many primes in the sequence[an] for almost all ? 相似文献
8.
Hayashi Nakao; Kaikina Elena I.; Naumkin Pavel I. 《Journal London Mathematical Society》2005,72(3):663-688
The Cauchy problem is studied for the nonlinear equations withfractional power of the negative Laplacian
where (0,2), with critical = /n and sub-critical (0,/n)powers of the nonlinearity. Let u0 L1,a L C, u0(x) 0 in Rn, = . The case of not small initial data is of interest. It is proved that the Cauchy problemhas a unique global solution u C([0,); L L1,a C) and the largetime asymptotics are obtained. 相似文献
9.
Let be a fixed open cube in Rn. For r[1, ) and [0, ) we define
where Q is a cube in Rn (with sides parallel to the coordinateaxes) and Q stands for the characteristic function of the cubeQ. A well-known result of Gehring [5] states that if
(1.1) for some p(1, ) and c(0, ), then there exist q(p, ) and C=C(p,q, n, c)(0, ) such that
for all cubes Q, where |Q| denotes the n-dimensional Lebesguemeasure of Q. In particular, a function fL1() satisfying (1.1)belongs to Lq(). In [9] it was shown that Gehring's result is a particular caseof a more general principle from the real method of interpolation.Roughly speaking, this principle states that if a certain reversedinequality between K-functionals holds at one point of an interpolationscale, then it holds at other nearby points of this scale. Usingan extension of Holmstedt's reiteration formulae of [4] andresults of [8] on weighted inequalities for monotone functions,we prove here two variants of this principle involving extrapolationspaces of an ordered pair of (quasi-) Banach spaces. As an applicationwe prove the following Gehring-type lemmas. 相似文献
10.
Haller-Dintelmann Robert; Heck Horst; Hieber Matthias 《Journal London Mathematical Society》2006,74(3):717-736
Consider a parabolic NxN-system of order m on n with top-ordercoefficients a VMOL. Let 1 < p, q < and let be a Muckenhouptweight. It is proved that systems of this kind possess a uniquesolution u satisfying
whereAu = ||m a Du and J = [0,). In particular, choosing = 1, therealization of A in Lp(n)N has maximal Lp – Lq regularity. 相似文献
11.
The existence of 2-periodic solutions of the second-order differentialequation
where a, b satisfy and p(t)=p(t+2),t R, is examined. Assume that limits limx±F(x)=F(±)(F(x)=) and limx±g(x)=g(±)exist and are finite. It is proved that the equation has atleast one 2-periodic solution provided that the zeros of thefunction 1 are simple and the zeros of the functions 1, 2 aredifferent and the signs of 2 at the zeros of 1 in [0,2/n) donot change or change more than two times, where 1 and 2 aredefined as follows:
Moreover, it is also proved that the given equation has at leastone 2-periodic solution provided that the following conditionshold:
with 1 p < q 2. 相似文献
12.
It is determined which Bloch-type conditions on a function f 0<p<Hp ensure that f BMOA. 相似文献
13.
Hochschild (Co)Homology Dimension 总被引:3,自引:0,他引:3
In 1989 Happel asked the question whether, for a finite-dimensionalalgebra A over an algebraically closed field k, gl.dim A < if and only if hch.dim A < . Here, the Hochschild cohomologydimension of A is given by hch.dim A := inf{n N0 | dim HHi(A) = 0 for i > n}. Recently Buchweitz, Green, Madsen andSolberg gave a negative answer to Happel's question. They founda family of pathological algebras Aq for which gl.dim Aq = but hch.dim Aq = 2. These algebras are pathological in manyaspects. However, their Hochschild homology behaviors are notpathological any more; indeed one has hh.dim Aq = = gl.dimAq. Here, the Hochschild homology dimension of A is given byhh.dim A := inf{n N0 | dim HHi(A) = 0 for i > n}. This suggestsposing a seemingly more reasonable conjecture by replacing theHochschild cohomology dimension in Happel's question with theHochschild homology dimension: gl.dim A < if and only ifhh.dim A < if and only if hh.dim A = 0. The conjecture holdsfor commutative algebras and monomial algebras. In the casewhere A is a truncated quiver algebra, these conditions areequivalent to the condition that the quiver of A has no orientedcycles. Moreover, an algorithm for computing the Hochschildhomology of any monomial algebra is provided. Thus the cyclichomology of any monomial algebra can be read off when the underlyingfield is characteristic 0. 相似文献
14.
On Some High-Indices Theorems II 总被引:1,自引:0,他引:1
15.
Let K be a function field of genus g with a finite constantfield Fq. Choose a place of K of degree and let C be the arithmeticDedekind domain consisting of all elements of K that are integraloutside . An explicit formula is given (in terms of q, g and) for the minimum index of a non-congruence subgroup in SL2(C).It turns out that this index is always equal to the minimumindex of an arbitrary proper subgroup in SL2(C). The minimumindex of a normal non-congruence subgroup is also determined. 相似文献
16.
Reducing Subspaces for a Class of Multiplication Operators 总被引:4,自引:0,他引:4
Let D be the open unit disk in the complex plane C. The Bergmanspace is the Hilbert space of analytic functions f in D such that
where dA is the normalized area measure on D. If
are two functions in , then the inner product of f and g is given by
We study multiplication operators on induced by analytic functions. Thus for H (D), the space ofbounded analytic functions in D, we define
by
It is easy to check that M is a bounded linear operator on with ||M||=||||=sup{|(z)|:zD}. 相似文献
17.
Let 1 < p < , 0 < v < p', let be a bounded domainin Rn, and denote by id the limiting compact embedding of theBesov space (Rn) into the exponentialOrlicz space Lexp(tv)(), mapping a function f onto its restrictionf|. In 1993 Triebel established, among others, two-sided estimatesfor the entropy numbers of id, which are even asymptoticallyoptimal for small . The aim of the paper is toimprove the upper bounds in the case of large, where Triebel's estimates are not yet sharp, thus making afurther step towards the conjectured correct asymptotic behaviour. 相似文献
18.
The (C,F)-construction from a previous paper of the first authoris applied to produce a number of funny rank one infinite measurepreserving actions of discrete countable Abelian groups G withunusual multiple recurrence properties. In particular,the following are constructed for each p N{}:
- a p-recurrent actionT=(Tg)gG such that (if p) no one transformationTg is (p+1)-recurrentfor every element g of infinite order;
- an action T=(Tg)gGsuch that for every finite sequence g1,...,grGwithout torsionthe transformation Tg1x...x Tgr is ergodic,p-recurrent but(if p) not (p+1)-recurrent;
- a p-polynomially recurrent (C,F)-transformationwhich (if p)is not (p+1)-recurrent.
19.
The Beurling algebras l1(D,)(D=N,Z) that are semi-simple, withcompact Gelfand transform, are considered. The paper gives anecessary and sufficient condition (on ) such that l1(D,) possessesa uniform quantitative version of Wiener's theorem in the sensethat there exists a function :]0,+[]0,+ such that, for everyinvertible element x in the unit ball of l1(D,), we have ||x1||(r(x1)) r(x1) is the spectral radiusof x1. 相似文献
20.
If = {1, 2, ..., s}, where 1 2 ... s > 0, is a partitionof n then denotes the associated irreducible character of Sn,the symmetric group on {1, 2, ..., n}, and, if cCSn, the groupalgebra generated by C and Sn, then dc(·) denotes thegeneralized matrix function associated with c. If c1, c2 CSnthen we write c1 c2 in case (A) (A) for each n x n positivesemi-definite Hermitian matrix A. If cCSn and c(e) 0, wheree denotes the identity in Sn, then or denotes (c(e))–1 c. The main result, an estimate for the norms of tensors of a certainanti-symmetry type, implies that if = {1, 2, ..., s, 1t} isa partition of n such that s > 1 and s = 2, and ' denotes{1, 2, ..., s-1, 1t} then (, {2}) where denotes characterinduction from Sn–2 x S2 to Sn. This in turn implies thatif = {1, 2, ..., s, 1t} with s > 1, s = 2, and ßdenotes {1 + 2, 2, ..., s-1, 1t} then ß which,in conjunction with other known results, provides many new inequalitiesamong immanants. In particular it implies that the permanentfunction dominates all normalized immanants whose associatedpartitions are of rank 2, a result which has proved elusivefor some years. We also consider the non-relationship problem for immanants– that is the problem of identifying pairs, (,ß)such that ß and ß are both false. 相似文献