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1.
In this paper, we first consider the problem of defining IFS operators on the space of non-empty compact and convex subsets of . After defining a complete metric on , we construct an IFS operator and show some properties. A notable feature is the definition of a type of weak inner product on . We then define a family of complete metrics on the space of all measurable set-valued functions (with values in ), and extend the weak inner product to this space. Following this, we construct IFS operators on these spaces. We close with a brief discussion of the inverse problem of approximating an arbitrary multifunction by the attractor of an IFS.  相似文献   

2.
A series is called a pointwise universal trigonometric series if for any , there exists a strictly increasing sequence of positive integers such that converges to f(z) pointwise on . We find growth conditions on coefficients allowing and forbidding the existence of a pointwise universal trigonometric series. For instance, if as |n|→∞ for some ε>0, then the series Sa cannot be pointwise universal. On the other hand, there exists a pointwise universal trigonometric series Sa with as |n|→∞.  相似文献   

3.
The paper deals with random vectors in , possessing the stochastic representation , where R is a positive random radius independent of the random vector and is a non-singular matrix. If is uniformly distributed on the unit sphere of , then for any integer m<d we have the stochastic representations and , with W≥0, such that W2 is a beta distributed random variable with parameters m/2,(dm)/2 and (U1,…,Um),(Um+1,…,Ud) are independent uniformly distributed on the unit spheres of and , respectively. Assuming a more general stochastic representation for in this paper we introduce the class of beta-independent random vectors. For this new class we derive several conditional limiting results assuming that R has a distribution function in the max-domain of attraction of a univariate extreme value distribution function. We provide two applications concerning the Kotz approximation of the conditional distributions and the tail asymptotic behaviour of beta-independent bivariate random vectors.  相似文献   

4.
We consider a triple of N-functions (M,H,J) that satisfy the Δ-condition, and suppose that an additive variant of interpolation inequality holds
where , is an arbitrary set invariant with respect to external and internal dilations. We show that the above inequality implies its certain nonlinear variant involving the expressions and . Various generalizations of this inequality to the more general class of N-functions, measures and to higher order derivatives are also discussed and the examples are presented.  相似文献   

5.
We prove that if a vector-function f belongs to the Morrey space , with , n≥3, N≥2, λ]0,n−2], and u is the solution of the system
then Du belongs to the space , for any , provided the matrix of bounded measurable coefficients (Aij) has sufficiently small dispersion of the eigenvalues.  相似文献   

6.
Let be any atomless and countably additive probability measure on the product space with the usual σ-algebra. Then there is a purely finitely additive probability measure λ on the power set of a countable subset such that can be isometrically isomorphically embedded as a closed subspace of Lp(λ). The embedding is strict. It is also ‘canonical,’ in the sense that it maps simple and continuous functions on to their restrictions to T.  相似文献   

7.
We prove that if K is a Gruenhage compact space then admits an equivalent, strictly convex dual norm. As a corollary, we show that if X is a Banach space and , where K is a Gruenhage compact in the w*-topology and |||||| is equivalent to a coarser, w*-lower semicontinuous norm on X*, then X* admits an equivalent, strictly convex dual norm. We give a partial converse to the first result by showing that if is a tree, then admits an equivalent, strictly convex dual norm if and only if is a Gruenhage space. Finally, we present some stability properties satisfied by Gruenhage spaces; in particular, Gruenhage spaces are stable under perfect images.  相似文献   

8.
Let Δ be the open unit disc in, let pbΔ, and let f be a continuous function on which extends holomorphically from each circle in centered at the origin and from each circle in which passes through p. Then f is holomorphic on Δ.  相似文献   

9.
We consider the following nonlinear elliptic equation with singular nonlinearity:
where α>β>1, a>0, and Ω is an open subset of , n2. Let uH1(Ω) with and be a nonnegative stationary solution. If we denote the zero set of u by
we shall prove that the Hausdorff dimension of Σ is less than or equal to .  相似文献   

10.
In this paper, it is defined the kth order Sobolev–Hardy space with norm
Then the corresponding Poincaré inequality in this space is obtained, and the results are given that this space is embedded in with weight and in with weight q/2 for 1q<2. Moreover, we prove that the constant of k-improved Hardy–Sobolev inequality with general weight is optimal. These inequalities turn to be some known versions of Hardy–Sobolev inequalities in the literature by some particular choice of weights.  相似文献   

11.
We study those filters on for which weak -convergence of bounded sequences in C(K) is equivalent to point-wise -convergence. We show that it is sufficient to require this property only for C[0,1] and that the filter-analogue of the Rainwater extremal test theorem arises from it. There are ultrafilters which do not have this property and under the continuum hypothesis there are ultrafilters which have it. This implies that the validity of the Lebesgue dominated convergence theorem for -convergence is more restrictive than the property which we study.  相似文献   

12.
Let H,V and K be separable Hilbert spaces. In this paper we consider the existence and uniqueness of energy solutions to the following stochastic evolution equation:
where is a linear bounded operator with coercivity, monotone condition and hemicontinuity, and are measurable functions and satisfy the local non-Lipschitz condition proposed by the author [T. Taniguchi, Successive approximations to solutions of stochastic differential equations, J. Differential Equations 96 (1992) 152–169].  相似文献   

13.
Oscillation of second-order damped dynamic equations on time scales   总被引:5,自引:0,他引:5  
The study of dynamic equations on time scales has been created in order to unify the study of differential and difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which may be an arbitrary closed subset of the reals. This way results not only related to the set of real numbers or set of integers but those pertaining to more general time scales are obtained. In this paper, by employing the Riccati transformation technique we will establish some oscillation criteria for second-order linear and nonlinear dynamic equations with damping terms on a time scale . Our results in the special case when and extend and improve some well-known oscillation results for second-order linear and nonlinear differential and difference equations and are essentially new on the time scales , h>0, for q>1, , etc. Some examples are considered to illustrate our main results.  相似文献   

14.
Let be the Laguerre hypergroup which is the fundamental manifold of the radial function space for the Heisenberg group. In this paper we obtain necessary and sufficient conditions on the parameters for the boundedness of the fractional maximal operator and the fractional integral operator on the Laguerre hypergroup from the spaces to the spaces and from the spaces to the weak spaces .  相似文献   

15.
Let denote the space of all upper triangular matrices A such that limr→1(1−r2)(A*C(r))B(2)=0. We also denote by the closed Banach subspace of consisting of all upper triangular matrices whose diagonals are compact operators. In this paper we give a duality result between and the Bergman–Schatten spaces . We also give a characterization of the more general Bergman–Schatten spaces , 1p<∞, in terms of Taylor coefficients, which is similar to that of M. Mateljevic and M. Pavlovic [M. Mateljevic, M. Pavlovic, Lp-behaviour of the integral means of analytic functions, Studia Math. 77 (1984) 219–237] for classical Bergman spaces.  相似文献   

16.
Let μ be a finite positive Borel measure with compact support consisting of an interval plus a set of isolated points in , such that μ>0 almost everywhere on [c,d]. Let , be a sequence of polynomials, , with real coefficients whose zeros lie outside the smallest interval containing the support of μ. We prove ratio and relative asymptotics of sequences of orthogonal polynomials with respect to varying measures of the form dμ/w2n. In particular, we obtain an analogue for varying measures of Denisov's extension of Rakhmanov's theorem on ratio asymptotics. These results on varying measures are applied to obtain ratio asymptotics for orthogonal polynomials with respect to fixed measures on the unit circle and for multi-orthogonal polynomials in which the measures involved are of the type described above.  相似文献   

17.
Let Ω be a regular domain in the complex plane , . Let be the linear space over of the holomorphic functions f in Ω such that f(n) is bounded in Ω and is continuously extendible to the closure of Ω, n=0,1,2,… . We endow , in a natural manner, with a structure of Fréchet space and we obtain dense subspaces F of , with good topological linear properties, also satisfying that each function f of F, distinct from zero, does not extend holomorphically outside Ω.  相似文献   

18.
Let be an operator algebra on a Hilbert space. We say that an element is an all-derivable point of for the strong operator topology if every strong operator topology continuous derivable linear mapping φ at G (i.e. φ(ST)=φ(S)T+Sφ(T) for any with ST=G) is a derivation. Let be a continuous nest on a complex and separable Hilbert space H. We show in this paper that every orthogonal projection operator P(M) () is an all-derivable point of for the strong operator topology.  相似文献   

19.
In this paper we present the necessary and sufficient conditions for linearizability of the planar time-reversible cubic complex system , . From these conditions, the necessary and sufficient conditions for the origin to be an isochronous center of the time-reversible cubic real system , can be obtained. Thus, the isochronous center problem of time-reversible cubic systems is solved completely.  相似文献   

20.
This paper deals with the existence of multiple positive solutions for the one-dimensional p-Laplacian subject to one of the following boundary conditions: or where φp(s)=|s|p−2s, p>1. By means of a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of at least three positive solutions. The interesting point is the nonlinear term f is involved with the first-order derivative explicitly.  相似文献   

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