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1.
In this paper, the spaceD p(Ω) of functions holomorphic on bounded symmetric domain ofC n is defined. We prove thatH p(Ω)⊂D p(Ω) if 0<p≤2, andD p(Ω)⊂H p(Ω) ifp≥2, and both the inclusions are proper. Further, we find that some theorems onH p(Ω) can be extended to a wider classD p(Ω) for 0<p≤2.  相似文献   

2.
Let (Ω,F, P) be a probability space and {F n}n≥0 a regular increasing sequence of sub-σ-fields ofF. LetH 1(Ω) be the usual Hardy space ofF n-martingales. We show that the couple (H 1(Ω),L (Ω)) is a partial retract of (L 1(Ω),L (Ω)). It is also proved that (L p(Ω),BMO(Ω)) is a partial retract of (L p(Ω),L (Ω)) for all 1<p<∞.  相似文献   

3.
Let Ω[ξ] denote the polynomial algebra (with 1) in commutative indeterminates {ie65-1}, 1 ≦i, jn, 1 ≦k < ∞, over a commutative ring Ω. Thealgebra of generic matrices Ω [Y] is defined to be the Ω-subalgebra ofM n (Ω[ξ]) generated by the matricesY k=({ie65-2}), 1 ≦i, jn, 1 ≦k < ∞. This algebra has been studied extensively by Amitsur and by Procesi in particular Amitsur has used it to construct a finite dimensional, central division algebra Ω (Y) which is not a crossed product. In this paper we shall prove, for Ω a domain, that Ω(Y) has exponentn in the Brauer group (Amitsur may already know this fact); consequently, for Ω an infinite field andn a multiple of 4, iff(X 1, …,X m) is a polynomial linear in all theX i but one (similar to Formanek’s central polynomials for matrix rings) andf 2 is central forM n (Ω), thenf is central forM n (Ω). (The existence of a polynomial not central forM n (Ω), but whose square is central forM n(Ω) is equivalent to every central division algebra of degreen containing a quadratic extension of its center; well-known theory immediately shows this is the case of 4‖n and 8χn.) Also, information is obtained about Ω(Y) for arbitary Ω, most notably that the Jacobson radical is the set of nilpotent elements. Partial support for this work was provided by National Science Foundation grant NSF-GP 33591.  相似文献   

4.
We prove a variant of a theorem of N. Alon and V. D. Milman. Using it we construct for everyn-dimensional Banach spacesX andY a measure space Ω and two operator-valued functionsT: Ω→L(X, Y),S: Ω→L(Y, X) so that ∫Ω S(ω)oT(ω) is the identity operator inX and ∫Ω||S(ω)||·||T(ω)||dω=O(n α ) for some absolute constantα<1. We prove also that any subset of the unitn-cube which is convex, symmetric with respect to the origin and has a sufficiently large volume possesses a section of big dimension isomorphic to ak-cube. Research supported in part by a grant of the Israel Academy of Sciences.  相似文献   

5.
Let (un)n≥0 be a non-degenerate linear recurrence sequence of integers. We show that the set of positive integersn such that either ω)(n) orΩ(n) dividesu n is of asymptotic density zero, where ω(n) and Ω(n) are the numbers of prime and prime power divisors ofn, respectively. The same also holds for the set of positive integersn such that τ(n)u n , where τ(n) is the number of the positive integer divisors of n, provided thatu n satisfies some mild technical conditions.  相似文献   

6.
The fundamental groups π 1 n ) of the spaces Ω n of generalized perfect splines are calculated. For n ≥ 2, the groups are trivial; π 11) is a free group with three generators.  相似文献   

7.
Let Ω and Π be two finitely connected hyperbolic domains in the complex plane \Bbb C{\Bbb C} and let R(z, Ω) denote the hyperbolic radius of Ω at z and R(w, Π) the hyperbolic radius of Π at w. We consider functions f that are analytic in Ω and such that all values f(z) lie in the domain Π. This set of analytic functions is denoted by A(Ω, Π). We prove among other things that the quantities Cn(W,P) := supf ? A(W,P)supz ? W\frac|f(n)(z)| R(f(z),P)n! (R(z,W))nC_n(\Omega,\Pi)\,:=\,\sup_{f\in A(\Omega,\Pi)}\sup_{z\in \Omega}\frac{\vert f^{(n)}(z)\vert\,R(f(z),\Pi)}{n!\,(R(z,\Omega))^n} are finite for all n ? \Bbb N{n \in {\Bbb N}} if and only if ∂Ω and ∂Π do not contain isolated points.  相似文献   

8.
We show that the maximal number of turns of anx-monotone path in an arrangement ofn lines is Ω(n 5/3) and the maximal number of turns of anx-monotone path in arrangement ofn pseudolines is Ω(n 2/logn).  相似文献   

9.
Let Ω be a bounded co.nvex domain in Rn(n≥3) and G(x,y) be the Green function of the Laplace operator -△ on Ω. Let hrp(Ω) = {f ∈ D'(Ω) :(E)F∈hp(Rn), s.t. F|Ω = f}, by the atom characterization of Local Hardy spaces in a bounded Lipschitz domain, the bound of f→(△)2(Gf) for every f ∈ hrp(Ω) is obtained, where n/(n 1)<p≤1.  相似文献   

10.
We show that in the worst case, Ω(n d ) sidedness queries are required to determine whether a set ofn points in ℝ d is affinely degenerate, i.e., whether it containsd+1 points on a common hyperplane. This matches known upper bounds. We give a straightforward adversary argument, based on the explicit construction of a point set containing Ω(n d ) “collapsible” simplices, any one of which can be made degenerate without changing the orientation of any other simplex. As an immediate corollary, we have an Ω(n d ) lower bound on the number of sidedness queries required to determine the order type of a set ofn points in ℝ d . Using similar techniques, we also show that Ω(n d+1) in-sphere queries are required to decide the existence of spherical degeneracies in a set ofn points in ℝ d . An earlier version of this paper was presented at the 34th Annual IEEE Symposium on Foundations of Computer Science [8]. This research has been supported by NSF Presidential Young Investigator Grant CCR-9058440.  相似文献   

11.
The boundedness of the commutator μΩ,b generalized by Marcinkiewicz integral μΩ and a function b(x) ∈ CBMOq(Rn) on homogeneous Morrey-Herz spaces is established.  相似文献   

12.
Let Ω be a domain in the extended complex plane such that ∞∈Ω . Further, let K= C / Ω and, for each n , let Q n be a monic polynomial of degree n with all its zeros in K . This paper is concerned with whether (Q n ) can be chosen so that, if f is any holomorphic function on Ω and P n is the polynomial part of the Laurent expansion of Q n f at , then (P n /Q n ) converges to f locally uniformly on Ω . It is shown that such a sequence (Q n ) can be chosen if and only if either K has zero logarithmic capacity or Ω is regular. January 21, 1999. Date accepted: August 17, 1999.  相似文献   

13.
Let Ω be a bounded domain of the complex plane whose boundary is a closed Jordan curve and (F n ) n≥0 the sequence of Faber polynomials of Ω. We say that a bounded linear operator T on a separable Banach space X is Ω-hypercyclic if there exists a vector x of X such that {F n (T)x: n ≥ 0} is dense in X. We show that many of the results in the spectral theory of hypercyclic operators involving the unit disk or its boundary have Ω-hypercyclic counterparts which involve the domain Ω or its boundary. The influence of the geometry of Ω or the smoothness of its boundary on Faber-hypercyclicity is also discussed.  相似文献   

14.
Let ? be the genealogical tree of a supercritical multitype Galton–Watson process, and let Λ be the limit set of ?, i.e., the set of all infinite self-avoiding paths (called ends) through ? that begin at a vertex of the first generation. The limit set Λ is endowed with the metric d(ζ, ξ) = 2 −n where n = n(ζ, ξ) is the index of the first generation where ζ and ξ differ. To each end ζ is associated the infinite sequence Φ(ζ) of types of the vertices of ζ. Let Ω be the space of all such sequences. For any ergodic, shift-invariant probability measure μ on Ω, define Ωμ to be the set of all μ-generic sequences, i.e., the set of all sequences ω such that each finite sequence v occurs in ω with limiting frequency μ(Ω(v)), where Ω(v) is the set of all ω′?Ω that begin with the word v. Then the Hausdorff dimension of Λ∩Φ−1μ) in the metric d is
almost surely on the event of nonextinction, where h(μ) is the entropy of the measure μ and q(i, j) is the mean number of type-j offspring of a type-i individual. This extends a theorem of HAWKES [5], which shows that the Hausdorff dimension of the entire boundary at infinity is log2 α, where α is the Malthusian parameter. Received: 30 June 1998 / Revised: 4 February 1999  相似文献   

15.
For an analytic function f on the hyperbolic domain Ω inC, the following conclusions are obtained: (i) f∈B(Ω)=BMO A(Ω,m) if and only ifRef∈Bh(Ω)=BMOH(Ω,m). (ii) QBh(Ω)=Bh(Ω)(BMOH n(Ω,m)=BMOH(Ω,m)) if and only ifC(Ω)=inf{λΩ(z)·δΩ(z):z∈Ω}>0. Also, some applications to automorphic functions are considered. This research was supported by the Doctoral Program Foundation of Institute of Higher Education.  相似文献   

16.
This paper proves an index theorem of Toeplitz tuples on pseudoregular domains in Cn. Geometrically, the index of Toeplitz tuple TΦn is (-1)n time wrapping number of Φn around the origin. As one of the applications of the index theorem, we completely characterize the automorphism groups of Toeplitz algebras on Poincaré domain. As another application, it is shown that C*(Ω)C*(Bn) for every Poincare domain Ω in Cn(n≠2). It is also noticed that C*(Ω)C*(B2) if and only if the Poincaré conjecture is true for Ω.  相似文献   

17.
Let Ω be an open subset of R d , d≥2, and let x∈Ω. A Jensen measure for x on Ω is a Borel probability measure μ, supported on a compact subset of Ω, such that ∫udμ≤u(x) for every superharmonic function u on Ω. Denote by J x (Ω) the family of Jensen measures for x on Ω. We present two characterizations of ext(J x (Ω)), the set of extreme elements of J x (Ω). The first is in terms of finely harmonic measures, and the second as limits of harmonic measures on decreasing sequences of domains. This allows us to relax the local boundedness condition in a previous result of B. Cole and T. Ransford, Jensen measures and harmonic measures, J. Reine Angew. Math. 541 (2001), 29–53. As an application, we give an improvement of a result by Khabibullin on the question of whether, given a complex sequence {α n } n=1 and a continuous function , there exists an entire function f≢0 satisfying f n )=0 for all n, and |f(z)|≤M(z) for all zC.  相似文献   

18.
We prove that the Schr?dinger equation defined on a bounded open domain of and subject to a certain attractive, nonlinear, dissipative boundary feedback is (semigroup) well-posed on L2(Ω) for any n = 1, 2, 3, ..., and, moreover, stable on L2(Ω) for n = 2, 3, with sharp (optimal) uniform rates of decay. Uniformity is with respect to all initial conditions contained in a given L2(Ω)-ball. This result generalizes the corresponding linear case which was proved recently in [L-T-Z.2]. Both results critically rely—at the outset—on a far general result of interest in its own right: an energy estimate at the L2(Ω)-level for a fully general Schr?dinger equation with gradient and potential terms. The latter requires a heavy use of pseudo-differential/micro-local machinery [L-T-Z.2, Section 10], to shift down the more natural H1(Ω)-level energy estimate to the L2(Ω)-level. In the present nonlinear boundary dissipation case, the resulting energy estimate is then shown to fit into the general uniform stabilization strategy, first proposed in [La-Ta.1] in the case of wave equations with nonlinear (interior and) boundary dissipation.  相似文献   

19.
Let φ(z) be an analytic function on a punctured neighborhood of ∞, where it has a simple pole. The nth Faber polynomial F n (z) (n=0,1,2,…) associated with φ is the polynomial part of the Laurent expansion at ∞ of [φ(z)] n . Assuming that ψ (the inverse of φ) conformally maps |w|>1 onto a domain Ω bounded by a piecewise analytic curve without cusps pointing out of Ω, and under an additional assumption concerning the “Lehman expansion” of ψ about those points of |w|=1 mapped onto corners of Ω, we obtain asymptotic formulas for F n that yield fine results on the limiting distribution of the zeros of Faber polynomials.   相似文献   

20.
Let P(D) be a partial differential operator with constant coefficients which is surjective on the space A(Ω) of real analytic functions on a covex open set Ω⊂ℝ n . Let L(P m ) denote the localizations at ∞ (in the sense of H?rmander) of the principal part P m . Then Q(x+iτN)≠ 0 for (x,τ)∈ℝ n ×(ℝ\{ 0}) for any QL(P m ) if N is a normal to δΩ which is noncharacteristic for Q. Under additional assumptions this implies that P m must be locally hyperbolic. Received: 24 January 2000  相似文献   

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