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1.
Let M be an invariant subspace of Hv2. It is shown that for each f∈M⊥, f can be analytically extended across (?)Bd\σ(Sz1,…, Szd).  相似文献   

2.
The authors study the existence of nontrivial solutions to p-Laplacian variational inclusion systems
$\left\{ \begin{gathered} - \Delta _p u + \left| u \right|^{p - 2} u \in \partial _1 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\ - \Delta _p v + \left| v \right|^{p - 2} v \in \partial _2 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\ \end{gathered} \right.$\left\{ \begin{gathered} - \Delta _p u + \left| u \right|^{p - 2} u \in \partial _1 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\ - \Delta _p v + \left| v \right|^{p - 2} v \in \partial _2 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\ \end{gathered} \right.  相似文献   

3.
Suppose that % MathType!End!2!1! is a variety of Lie algebras, and letc n( % MathType!End!2!1!) be the dimension of the linear span of all multilinear words onn distinct letters in the free algebraF( % MathType!End!2!1!,X) of the variety % MathType!End!2!1!. We consider an exponential generating function % MathType!End!2!1!, called the complexity function. The complexity function is an entire function of a complex variable provided the variety of Lie algebras is nontrivial. In this paper we introduce the notion of complexity for Lie varieties in terms of the growth of complexity functions; also we describe what the complexity means for the codimension growth of the variety. Our main goal is to specify the complexity of a product of two Lie varieties in terms of the complexities of multiplicands. The main observation here is thatC( % MathType!End!2!1!),z) behaves like a composition of three functionsC( % MathType!End!2!1!),z), exp(z), andC( % MathType!End!2!1!),z). Partially supported by grant RFFI 96-01-00146; the author is grateful to the University of Bielefeld for hospitality, where he was DAAD-fellow.  相似文献   

4.
Let be an arbitrary division ring and M n ( ) the multiplicative semigroup of all n × n matrices over . We describe the general form of endomorphisms of M n ( ). Supported in part by a grant from the Ministry of Science of Slovenia.  相似文献   

5.
Summary We present a Fitting Class construction which exploits the properties of a certain class of finite soluble groups of nilpotent length three, called -groups in the paper. In addition we look at a wider class of groups, called in the paper, also of nilpotent length three and examine the question as to what -groups are in .A number of examples are given to illuminate the various classes.The author would like to thank HermannHeineken for supervising his dissertation, from which this paper has sprung, the German Academic Exchange Service (DAAD) for enabling him to study with Prof. Heineken at Universität Würzburg and An Roinn Oideachais for the fellowship which is at present supporting him at University College, Galway.  相似文献   

6.
Conformal CMC-Surfaces in Lorentzian Space Forms   总被引:1,自引:1,他引:0  
Let Q3 be the common conformal compactification space of the Lorentzian space forms R13, S13 and H13. We study the conformal geometry of space-like surfaces in Q3. It is shown that any conformal CMC-surface in Q3 must be conformally equivalent to a constant mean curvature surface in R13, S13 or H13. We also show that if x : M→Q3 is a space-like Willmore surface whose conformal metric g has constant curvature K, then either K = - 1 and x is conformally equivalent to a minimal surface in R13, or K = 0 and x is conformally equivalent to the surface H1(1/(2~(1/2)))×H1(1/(2~(1/2))) in H13.  相似文献   

7.
Let T be a transcendental element of and the orbit of T. On we have a Haar measure . The goal of this paper is to characterize all the elements of for which the integral , called the trace of T, is well defined.Presented by A. Verschoren  相似文献   

8.
Let f(n) be a strongly additive complex-valued arithmetic function. Under mild conditions on f, we prove the following weighted strong law of large numbers: if X,X 1,X 2, … is any sequence of integrable i.i.d. random variables, then
$ \mathop {\lim }\limits_{N \to \infty } \frac{{\sum\nolimits_{n = 1}^N {f(n)X_n } }} {{\sum\nolimits_{n = 1}^N {f(n)} }} = \mathbb{E}Xa.s. $ \mathop {\lim }\limits_{N \to \infty } \frac{{\sum\nolimits_{n = 1}^N {f(n)X_n } }} {{\sum\nolimits_{n = 1}^N {f(n)} }} = \mathbb{E}Xa.s.   相似文献   

9.
10.
Let $ \mathbb{B} $ \mathbb{B} be the unit ball in ℂ n and let H($ \mathbb{B} $ \mathbb{B} ) be the space of all holomorphic functions on $ \mathbb{B} $ \mathbb{B} . We introduce the following integral-type operator on H($ \mathbb{B} $ \mathbb{B} ):
$ I_\phi ^g (f)(z) = \int\limits_0^1 {\operatorname{Re} f(\phi (tz))g(tz)\frac{{dt}} {t}} ,z \in \mathbb{B}, $ I_\phi ^g (f)(z) = \int\limits_0^1 {\operatorname{Re} f(\phi (tz))g(tz)\frac{{dt}} {t}} ,z \in \mathbb{B},   相似文献   

11.
In 1993,Ahern,Flores and Rudin showed that,if f is integrable over the unit ball BC^n of C^n and satisfies∫BC^nfoφdv=f(φ(0)) for every φ∈Aut(BC^n),then f is M-harmonic if and only if n≤11.The present paper is about an analogous question in the context of the unit ball Bn of R^n as well as in the weighted setting.  相似文献   

12.
In this paper, we prove the estimate
, for every δ ∈ (0, ℓN), where C = C(N) is a positive constant depending only on N and . We show that the constant ℓN in this estimate is optimal. We also present a class of maps from into , strictly larger than , on which we can define the notion of degree and for which the previous inequality still holds.  相似文献   

13.
A group G has finite rank r if every finitely generated subgroup of G is at most r-generator. If C is a class of groups then we let C* denote the class of groups G in which every proper subgroup of G is either of finite rank or in C. We let denote the class of soluble groups and the class of soluble groups of derived length at most d, where d is a positive integer. We let λ denote the set of closure operations and let denote the λ-closure of the class of periodic locally graded groups. Amongst other results we prove that a soluble -group is either of finite rank or of derived length at most d and also that a group in the class is either locally soluble, or has finite rank, or is isomorphic to one of or for suitable locally finite fields . The second author would like to thank the Department of Mathematics at Bucknell University for its hospitality while part of this work was being done.  相似文献   

14.
We consider the solutions of refinement equations written in the form
where the vector of functions ϕ = (ϕ 1, ..., ϕ r ) T is unknown, g is a given vector of compactly supported functions on ℝ s , a is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s dilation matrix with m = |detM|. Inhomogeneous refinement equations appear in the construction of multiwavelets and the constructions of wavelets on a finite interval. The cascade algorithm with mask a, g, and dilation M generates a sequence ϕ n , n = 1, 2, ..., by the iterative process
from a starting vector of function ϕ 0. We characterize the L p -convergence (0 < p < 1) of the cascade algorithm in terms of the p-norm joint spectral radius of a collection of linear operators associated with the refinement mask. We also obtain a smoothness property of the solutions of the refinement equations associated with the homogeneous refinement equation. This project is supported by the NSF of China under Grant No. 10071071  相似文献   

15.
We define a cohomological invariantE(G, S, M) whereG is a group,S is a non empty family of (not necessarily distinct) subgroups of infinite index inG andM is a -module ( is the field of two elements). In this paper we are interested in the special case where the family of subgroups consists of just one subgroup, andM is the -module . The invariant will be denoted byE(G, S). We study the relations of this invariant with other endse(G), e(G, S) ande(G,S)), and some results are obtained in the case whereG andS have certain properties of duality.  相似文献   

16.
We study the Hardy-Littlewood maximal operator M on . Under the assumptions that the exponent p satisfies and is constant outside some large ball, we prove that if and only if . Received: 2 June 2006 Revised: 28 November 2006  相似文献   

17.
Let be the Heisenberg group and μ r be the normalized surface measure on the sphere of radiusr in ℂ n . Let . We prove an optimalL p-boundedness result for the spherical maximal functionMf, namely we prove thatM is bounded onL p(I n ) if and only ifp>2n/2n−1.  相似文献   

18.
Natural bounded concentrators   总被引:1,自引:0,他引:1  
We give the first known direct construction for linear families of bounded concentrators. The construction is explicit and the results are simple natural bounded concentrators. Let be the field withq elements,g(x)F q [x] of degree greater than or equal to 2, and . LetI nputs=H/A,O utputs=H/B, and draw an edge betweenaA andbB iffaA∩bB≠ϕ. We prove that for everyq≥5 this graph is an concentrator. Part of this research was done while the author was at the department of Computer Science, The University of British Columbia, Vancouver, B.C., Canada.  相似文献   

19.
Let λ(n) be the Liouville function. We find a nontrivial upper bound for the sum
$ \sum\limits_{X \leqslant n \leqslant 2X} {\lambda (n)e^{2\pi i\alpha \sqrt n } } ,0 \ne \alpha \in \mathbb{R} $ \sum\limits_{X \leqslant n \leqslant 2X} {\lambda (n)e^{2\pi i\alpha \sqrt n } } ,0 \ne \alpha \in \mathbb{R}   相似文献   

20.
Let be a boolean function, and suppose that the spectral norm of f is at most M. Then where and each H j is a subgroup of . This result may be regarded as a quantitative analogue of the Cohen-Helson-Rudin structure theorem for idempotent measures in locally compact abelian groups. Received: May 2006 Accepted: January 2007  相似文献   

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