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1.
Let be an infinitely divisible probability measure onR n without Gaussian component and let be its Lévy measure. Suppose that is absolutely continuous with respect to the Lebesgue measure . We investigate the structure of the set n of admissible translates of . This yields a unified presentation of previously known results. We also show that if(S)>0 then is equivalent to , under the assumption that supp =R n , whereS is the closure of the semigroup generated by the support of .The research of this author is supported by KBN Grant.The research of this author is supported by AFSOR Grant No. 90-0168, and the University of Tennessee Science Alliance, a State of Tennessee Center of Excellence.  相似文献   

2.
We prove a local limit theorem (LLT) on Cramer-type large deviations for sums S V = t V ( t ), where t , t Z , 1, is a Markov Gaussian random field, V Z , and is a bounded Borel function. We get an estimate from below for the variance of S V and construct two classes of functions , for which the LLT of large deviations holds.  相似文献   

3.
Canonical representations on Hermitian symmetric spaces G/K were introduced by Vershik, Gelfand and Graev and Berezin. They are unitary. We study canonical representations in a wider sense. In this paper we restrict ourselves to a crucial example – the Lobachevsky plane: G=SU(1,1), K=U(1). Canonical representations are labelled by the complex parameter (Vershik–Gelfand–Graev's representations correspond to –3/2<<0). We decompose the canonical representations into irreducible components. The decomposition includes boundary representations generated by the canonical representations. So we study these boundary representations themselves. The decomposition of boundary representations is closely connected with the meromorphic structure of Poisson and Fourier transforms associated with canonical representations. In particular, second-order poles give second-order Jordan blocks. Finally, we give a full decomposition of the Berezin transform using generalized powers (Pochhammer symbols) instead of usual powers of .  相似文献   

4.
Following earlier work of Tits [8], this paper deals with the structure of buildings which are not necessarily thick; that is, possessing panels (faces of codimension 1) which are contained in two chambers, only. To every building , there is canonically associated a thick building whose Weyl group W( ) can be considered as a reflection subgroup of the Weyl group W() of . One can reconstruct from together with the embedding W( ) W(). Conversely, if is any thick building and W any reflection group containing W( ) as a reflection subgroup, there exists a weak building with Weyl group W and associated thick building .  相似文献   

5.
In this paper we study particular sets of a Steiner systemS. More precisely, we study the setsA such that ¦A ¦ d modh for all lines ofS, withd andh integers satisfyingd 0,h 2.Dedicated to Professor M. Scafati Tallini on the occasion of her sixtyfifth birthday  相似文献   

6.
Leta be irrational and letf:[0,1] be Riemann-integrable with integral zero. Letf n (x) denote the Weyl sumf n (x):= k=0 n–1 f({x k>}),x/[0,1[,n. We prove criteria for the boundedness of the sequence (f n ) n1 and discuss the relation of this question to irregularities of the distribution of sequences.  相似文献   

7.
— [0,1] ,E — - e=1 [0,1]. I — E =1, E=L 2 x e =xL 2 x E.

This work was prepared when the second author was a visiting professor of the CNR at the University of Firenze. He was supported by the Soros International Fund.  相似文献   

8.
G- p- . [5] - (G) L r(G) (1r<), . . , - . , , , . . , X. , . (. [1], [2] [4]).  相似文献   

9.
Summary For differential operatorsM of second order (as defined in (1.1)) we describe a method to prove Range-Domain implications—Muu and an algorithm to construct these functions , , , . This method has been especially developed for application to non-inverse-positive differential operators. For example, for non-negativea 2 and for given functions = we require =C 0[0, 1] C 2([0, 1]–T) whereT is some finite set), (M) (t)(t), (t[0, 1]–T) and certain additional conditions for eachtT. Such Range-Domain implications can be used to obtain a numerical error estimation for the solution of a boundary value problemMu=r; further, we use them to guarantee the existence of a solution of nonlinear boundary value problems between the bounds- and .  相似文献   

10.
Using a capacity approach, we prove in this article that it is always possible to define a realization of the Laplacian on L 2() with generalized Robin boundary conditions where is an arbitrary open subset of R n and is a Borel measure on the boundary of . This operator generates a sub-Markovian C 0-semigroup on L 2(). If d=d where is a strictly positive bounded Borel measurable function defined on the boundary and the (n–1)-dimensional Hausdorff measure on , we show that the semigroup generated by the Laplacian with Robin boundary conditions has always Gaussian estimates with modified exponents. We also obtain that the spectrum of the Laplacian with Robin boundary conditions in L p () is independent of p[1,). Our approach constitutes an alternative way to Daners who considers the (n–1)-dimensional Hausdorff measure on the boundary. In particular, it allows us to construct a conterexample disproving Daners' closability conjecture.  相似文献   

11.
Summary LetG be a separable locally compact group with dual space. consists of all equivalence classes of irreducible unitary representations ofG, and is endowed with the Fell-topology. We study the topological properties in of the square-integrable representations ofG. [ is square-integrable provided there is a coordinate functiong((g)v, v),gG, for which is inL 2(G) w.r.t. left Haar measure onG.]SupposeG contains an open normal subgroupN of the formeKN n e whereK is compact. (All groups with a compact invariant neighborhood of the identity, [IN] groups, satisfy this condition.) In this case we show that if is square-integrable then {} is an open point of.Finally, our techniques are used to prove this result for arbitrary (non connected) nilpotent Lie groups.  相似文献   

12.
We consider a functional differential equation (1) (t)=F(t,) fort[0,+) together with a generalized Nicoletti condition (2)H()=. The functionF: [0,+)×C 0[0,+)B is given (whereB denotes the Banach space) and the value ofF (t, ) may depend on the values of (t) fort[0,+);H: C 0[0,+)B is a given linear operator and B. Under suitable assumptions we show that when the solution :[0,+)B satisfies a certain growth condition, then there exists exactly one solution of the problem (1), (2).  相似文献   

13.
For any two primes, , such that< and divides–1, it is shown that there exists a non-Moufang Bol loop of order 2 which is isomorphic to each of its loop isotopes.  相似文献   

14.
—.

Dedicated to Professor L. Leindler on his 50th birthday  相似文献   

15.
Harold L. Putt 《Order》1984,1(2):173-185
In this note we discuss permutation groups (G, ) in which the set admits aG-invariant order. By aG-invariant partial order (G-partial order) we mean a partial order < of such that < implies g<g, for all and in andg inG. If the set admits aG-partial order which is a total order, then (G, ) is an O-permutation group (orderable permutation group).The main concern of this paper is the development of a foundation for partially ordered permutation groups analogous to the existing one for partially ordered groups, as found in Fuchs [2].  相似文献   

16.
Let A be a set of positive integers with gcd (A) = 1, and let p A (n) be the partition function of A. Let c 0 = 2/3. If A has lower asymptotic density and upper asymptotic density , then lim inf log p A (n)/c 0 n and lim sup log p A (n)/c 0 n . In particular, if A has asymptotic density > 0, then log p A (n) c0n. Conversely, if > 0 and log p A (n) c 0 n, then the set A has asymptotic density .  相似文献   

17.
18.
Let X be a Banach space with a countable unconditional basis (e.g., X=2), X open. We show that is pseudoconvex if and only if for each affine complex line L in X the sheaf cohomology group H 1 (,I) vanishes, where I is the ideal sheaf of all holomorphic functions on that vanish on L. We also give an example that the condition H q (,)=0 for all q1 unlike in finite dimensions does not imply the pseudoconvexity of . Lastly, we prove an interpolation result. Mathematics Subject Classification (2002): 32T05, 46G20.  相似文献   

19.
20.
A measure for the denseness of sequences (an) mod 1, irrational, is the dispersion constantD() introduced byH. Niederreiter. In this paper the smallest accumulation point 1 of the set of theD() is determined and all those are explicitely given for whichD () < 1 holds.  相似文献   

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