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1.
We study in this paper some relations between Hardy spaces which are defined by non-smooth approximate identity ?(x), and the end-point Triebel-Lizorkin spaces (1?q?∞). First, we prove that for compact ? which satisfies a slightly weaker condition than Fefferman and Stein's condition. Then we prove that non-trivial Hardy space defined by approximate identity ? must contain Besov space . Thirdly, we construct certain functions and a function such that Daubechies wavelet function but .  相似文献   

2.
Let , where is a random symmetric matrix, a random symmetric matrix, and with being independent real random variables. Suppose that , and are independent. It is proved that the empirical spectral distribution of the eigenvalues of random symmetric matrices converges almost surely to a non-random distribution.  相似文献   

3.
Let Un be an extended Tchebycheff system on the real line. Given a point , where x1<?<xn, we denote by the polynomial from Un, which has zeros x1,…,xn. (It is uniquely determined up to multiplication by a constant.) The system Un has the Markov interlacing property (M) if the assumption that and interlace implies that the zeros of and interlace strictly, unless . We formulate a general condition which ensures the validity of the property (M) for polynomials from Un. We also prove that the condition is satisfied for some known systems, including exponential polynomials and . As a corollary we obtain that property (M) holds true for Müntz polynomials , too.  相似文献   

4.
Generalized cross-validation (GCV) is a widely used parameter selection criterion for spline smoothing, but it can give poor results if the sample size n is not sufficiently large. An effective way to overcome this is to use the more stable criterion called robust GCV (RGCV). The main computational effort for the evaluation of the GCV score is the trace of the smoothing matrix, , while the RGCV score requires both and . Since 1985, there has been an efficient O(n) algorithm to compute . This paper develops two pairs of new O(n) algorithms to compute and , which allow the RGCV score to be calculated efficiently. The algorithms involve the differentiation of certain matrix functionals using banded Cholesky decomposition.  相似文献   

5.
In this paper we initiate the study of composition operators on the noncommutative Hardy space , which is the Hilbert space of all free holomorphic functions of the form
  相似文献   

6.
A well-known polymodal provability logic due to Japaridze is complete w.r.t. the arithmetical semantics where modalities correspond to reflection principles of restricted logical complexity in arithmetic. This system plays an important role in some recent applications of provability algebras in proof theory. However, an obstacle in the study of is that it is incomplete w.r.t. any class of Kripke frames. In this paper we provide a complete Kripke semantics for . First, we isolate a certain subsystem of that is sound and complete w.r.t. a nice class of finite frames. Second, appropriate models for are defined as the limits of chains of finite expansions of models for . The techniques involves unions of n-elementary chains and inverse limits of Kripke models. All the results are obtained by purely modal-logical methods formalizable in elementary arithmetic.  相似文献   

7.
For sets given as finite intersections the basic normal cone is given as , but such a result is not, in general, available for infinite intersections. A comparable characterization of is obtained here for a class of such infinite intersections.  相似文献   

8.
The paper considers a slightly modified notion of the Γ-convergence of convex functionals in uniformly convex Banach spaces and establishes that under standard coercitivity and growth conditions the Γ-convergence of a sequence of functionals {Fj} to implies that the corresponding sequence of dual functionals converges in an analogous sense to the dual to functional .  相似文献   

9.
Bi-Sobolev mappings have been defined as those homeomorphisms such that f and f−1 belong to . We deduce regularity properties of the distortion of f from the regularity of the differential matrix Df−1 and conversely.  相似文献   

10.
We show that the absolute numerical index of the space Lp(μ) is (where ). In other words, we prove that
  相似文献   

11.
We compute the limiting subdifferential of the indefinite integral of the form where f is an essentially bounded measurable function, or a function continuous on an interval containing (except for, possibly, ), or a step-function which has a countable number of steps around . The related problem of computing the Aumann integral of the limiting subdifferential mapping ∂f(⋅), where f is a Lipschitz real function defined on an open set URn, is also investigated.  相似文献   

12.
13.
We consider the Yamabe equation in Rn, n?3. Let k?1 and . For all large k we find a solution of the form , where , for n?4, for n=3 and o(1)→0 uniformly as k→+∞.  相似文献   

14.
Let 1?n?∞, and let be a row contraction on some Hilbert space H. Let F(T) be the space of all XB(H) such that . We show that, if non-zero, this space is completely isometric to the commutant of the Cuntz part of the minimal isometric dilation of .  相似文献   

15.
We consider tensors T=fg on the pseudo-euclidean space Rn and on the hyperbolic space Hn, where n?3, g is the standard metric and f is a differentiable function. For such tensors, we consider, in both spaces, the problems of existence of a Riemannian metric , conformal to g, such that , and the existence of such a metric which satisfies , where is the scalar curvature of . We find the restrictions on the Ricci candidate for solvability and we construct the solutions when they exist. We show that these metrics are unique up to homothety, we characterize those globally defined and we determine the singularities for those which are not globally defined. None of the non-homothetic metrics , defined on Rn or Hn, are complete. As a consequence of these results, we get positive solutions for the equation , where g is the pseudo-euclidean metric.  相似文献   

16.
We consider positive solutions of on B1 (n?5) where μ and K>0 are smooth functions on B1. If K is very sub-harmonic at each critical point of K in B2/3 and the maximum of u in is comparable to its maximum over , then all positive solutions are uniformly bounded on . As an application, a priori estimate for solutions of equations defined on Sn is derived.  相似文献   

17.
We give a geometric interpretation of the Weil representation of the metaplectic group, placing it in the framework of the geometric Langlands program.For a smooth projective curve X we introduce an algebraic stack of metaplectic bundles on X. It also has a local version , which is a gerbe over the affine Grassmanian of G. We define a categorical version of the (nonramified) Hecke algebra of the metaplectic group. This is a category of certain perverse sheaves on , which act on by Hecke operators. A version of the Satake equivalence is proved describing as a tensor category. Further, we construct a perverse sheaf on corresponding to the Weil representation and show that it is a Hecke eigen-sheaf with respect to .  相似文献   

18.
For a pseudovariety of ordered semigroups, let be the class of sofic subshifts whose syntactic semigroup lies in . It is proved that if contains then is closed under taking shift equivalent subshifts, and conversely, if is closed under taking conjugate subshifts then contains and . Almost finite type subshifts are characterized as the irreducible elements of , which gives a new proof that the class of almost finite type subshifts is closed under taking shift equivalent subshifts.  相似文献   

19.
We consider the semilinear elliptic problem in Ω, u=0 on ∂Ω, where 0∈Ω is a smooth bounded domain in RN, N?4, , is the critical Sobolev exponent, f(x,⋅) has subcritical growth at infinity, K(x)>0 is continuous. We prove the existence of sign-changing solutions under different assumptions when Ω is a usual domain and a symmetric domain, respectively.  相似文献   

20.
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