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1.
We study Toeplitz operators on the harmonic Bergman spaceb p (B), whereB is the open unit ball inR n(n2), for 1<p. We give characterizations for the Toeplitz operators with positive symbols to be bounded, compact, and in Schatten classes. We also obtain a compactness criteria for the Toeplitz operators with continuous symbols.  相似文献   

2.
Let 1<p< and . LetC q denote the Bessel capacity in the plane. Let be the set of homomorphisms ofH (G) such that (z)= and letNP denote the set of points in G for which is not a peak set forH (G). In this note, we show that ifC q (NP)=0, thenH (G) is dense inL a p (G), the Bergman space overG.Partially supported by NSF DMS-9401234  相似文献   

3.
We give a new2 index theorem for the basic example of Toeplitz operators on the circle. The joint torsion, a non zero complex valued analytic index, of a pair of Fredholm Toeplitz operatorsT andT withH symbols is computed by residues in the disk, and is determined by a monodromy integral which specifies the isomorphism class of a flat line bundle on the circle. When the symbols and are rational a product of joint torsions identifies the isomorphism class of the bundle inH 1 (S 1,C *), and the identification extends by rational approximation to the case of smooth symbols defined on the circle.Partially supported by National Science Foundation grants to both authors.  相似文献   

4.
On log-hyponormal operators   总被引:9,自引:0,他引:9  
LetTB(H) be a bounded linear operator on a complex Hilbert spaceH.TB(H) is called a log-hyponormal operator itT is invertible and log (TT *)log (T * T). Since log: (0, )(–,) is operator monotone, for 0<p1, every invertiblep-hyponormal operatorT, i.e., (TT *) p (T * T) p , is log-hyponormal. LetT be a log-hyponormal operator with a polar decompositionT=U|T|. In this paper, we show that the Aluthge transform is . Moreover, ifmeas ((T))=0, thenT is normal. Also, we make a log-hyponormal operator which is notp-hyponormal for any 0<p.This research was supported by Grant-in-Aid Research No. 10640185  相似文献   

5.
In this paper, we prove that the Hardy spaceH p (), 1p<, over a strictly pseudoconvex domain in n with smooth boundary is quasi-coherent. More precisely, we show that Toeplitz tuplesT with suitable symbols onH p () have property (). This proof is based on a well known exactness result for the tangential Cauchy-Riemann complex.  相似文献   

6.
If belongs to the essential approximate point spectrum of a Banach space operatorTB(X) and is a sequence of positive numbers with lim j a j =0, then there existsxX such that for every polynomialp. This result is the best possible — if for some constantc>0 thenT has already a non-trivial invariant subspace, which is not true in general.  相似文献   

7.
A new criterion of solvability of the interpolation problem f( n )=bn in the class of functions f, analytic in the right half-plane and such that there exists c 1(0;+) such that |f(z)|c 1exp((c1|z|)) for all z , where is a positive increasing continuous differentiable function on [0;+), for which (t)+ as t+ and there exists c 2(0;+) such that
for all t 1 is described.  相似文献   

8.
In this paper, we will use the Birkhoff's ergodic theorem to do some finer analysis on the spectral properties of slant Toeplitz operators. For example, we will show that if is an invertibleL function on the unit circle, then almost every point in (A * ) is not an eigenvalue ofA * . More specifically, we will show that the point spectrum ofA * is contained in a circle with positive radius.  相似文献   

9.
Let * be the convolution on M( +) associated with a second order singular differential operator L on ]0, +[. If is a probability measure on + with suitable moment conditions, we study how to normalize the measures * n ; n } (resp. ) in order to get vague convergence if n+ (resp. x+). The results depend on the asymptotic drift of the operator L and on a precise study of the asymptotic behaviour of its eigenfunctions.  相似文献   

10.
This paper is devoted to an approximation problem for operators in Hilbert space, that appears when one tries to study geometrically thecascade algorithm in wavelet theory. Let be a Hilbert space, and let be a representation ofL ( ) on . LetR be a positive operator inL ( ) such thatR(1) =1, where1 denotes the constant function 1. We study operatorsM on (bounded, but noncontractive) such that
where the * refers to Hilbert space adjoint. We give a complete orthogonal expansion of which reduces such thatM acts as a shift on one part, and the residual part is () = n [M n ], where [M n ] is the closure of the range ofM n . The shift part is present, we show, if and only if ker (M *){0}. We apply the operator-theoretic results to the refinement operator (or cascade algorithm) from wavelet theory. Using the representation , we show that, for this wavelet operatorM, the components in the decomposition are unitarily, and canonically, equivalent to spacesL 2(E n ) L 2(), whereE n , n=1,2,3,..., , are measurable subsets which form a tiling of ; i.e., the union is up to zero measure, and pairwise intersections of differentE n 's have measure zero. We prove two results on the convergence of the cascale algorithm, and identify singular vectors for the starting point of the algorithm.Terminology used in the paper     the one-torus -   Haar measure on the torus - Z   the Zak transform - X=ZXZ –1   transformation of operators -   a given Hilbert space -   a representation ofL ( ) on - R   the Ruelle operator onL ( ) - M   an operator on - R *,M *   adjoint operators Work supported in part by the U.S. National Science Foundation.  相似文献   

11.
Athreya  Siva 《Potential Analysis》2002,17(3):293-301
On a bounded C 2-domain we consider the singular boundary-value problem 1/2u=f(u) in D, u D =, where d3, f:(0,)(0,) is a locally Hölder continuous function such that f(u) as u0 at the rate u , for some (0,1), and is a non-negative continuous function satisfying certain growth assumptions. We show existence of solutions bounded below by a positive harmonic function, which are smooth in D and continuous in . Such solutions are shown to satisfy a boundary Harnack principle.  相似文献   

12.
For C a bounded, injective operator with dense image, we define a C-regularized spectral distribution. This produces a functional calculus, f f(B), from C() into the space of closed densely defined operators, such that f(B)C is bounded when f has compact support. As an analogue of Stone's theorem, we characterize certain regularized spectral distributions as corresponding to generators of polynomially bounded C-regularized groups. We represent the regularized spectral distribution in terms of the regularized group and in terms of the C-resolvent. Applications include the Schrödinger equation with potential, and symmetric hyperbolic systems, all on Lp(n) (1p<), C o(n), BUC(n), or any space of functions where translation is a bounded strongly continuous group.  相似文献   

13.
We prove that a weakly compact operator fromH or any of its even duals into an arbitrary Banach space is uniformly convexifying. By using this, we establish three dicothomies: (1) every operator defined onH or any of its even duals either fixes a copy ofl or factors through a Banach space having the Banach-Saks property; (2) every quotient ofH or any of its even duals either contains a copy ofl or is super-reflexive; (3) every subspace ofL 1/H 0 1 or any of its even duals either contains a complemented copy ofl 1 or is super-reflexive.  相似文献   

14.
Let denote the set of analytic bounded point evaluations forR q (K, ). Assume that . In this paper, we first show that if is a finitely connected domain and if the evaluation map fromR q (K, )L () toH () is surjective, then | is absolutely continuous with respect to harmonic measure for . This generalizes Olin and Yang's corresponding result for polynomials and the proof we present here is simpler. We also provide an example that shows this absolute continuity property fails in general when is an infinitely connected domain. In the second part, we then offer a solution to a problem of Conway and Elias.  相似文献   

15.
It is shown that the algebra of the multipliers of the space p (1<<) contains the closed subalgebra Cp+H p , which coincides with the Douglas algebra C + H for =2. It is proved that a Toeplitz operator with symbol from Cp+H p is Fredholm on p if and only if its symbol is invertible in Cp+H p .Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 157, pp. 124–128, 1987.The authors are grateful to V. I. Vasyunin for assistance.  相似文献   

16.
We investigate problems related to the approximation by linear methods and the best approximations of the classes , 1 p in the space L .  相似文献   

17.
LetA andB be two anticommuting self-adjoint operators andV() be a symmetric operator in a Hilbert space, where >0 is a parameter. It is proven that, under some conditions forV(), the resolvents of A+2 B±2|B|+V() converge as . Applications to the nonrelativistic-limit problem of Dirac operators and supersymmetry are discussed.This work is supported by the Grant-In-Aid 0560139 for science research from the Ministry of Education, Japan.  相似文献   

18.
In this paper we show that theH 2 minimization of theH suboptimal solutions for a class of suboptimalH distance problems can be reduced to a finite dimensional nonlinear optimization problem. This extends a result of [7] where the same problem is considered in the Caratheodory-Schur interpolation case.  相似文献   

19.
In this note we show that theH 2 optimization of theH interpolant in the Carathéodory-Schur problem reduces to a finite dimensional albeit very nonlinear problem. Moreover we prove that theH 2-optimalH interpolant can be rational only in the trivial case, namely when it coincides with the original given polynomial.  相似文献   

20.
Summary We prove some regularity results for the solution of a linear abstract Cauchy problem of parabolic type. As an application, we study the approximation of the solution by means of an implicit-Euler discretization in time, which is stable with respect to a wide class of Galerkin approximation methods in space. The error is evaluated in norms of typeL 2(0, ,L 2) andL 2(0, ,V)(H 00 1/2 (0, ,H)+H 1(0, ,V)), whereVHV are Hilbert spaces (the embeddings are supposed to be dense and continuous). We prove error estimates which are optimal with respect to the regularity assumptions on the right-hand side of the equation.The author was supported by G.N.A.F.A. and I.A.N. of C.N.R. and by M.P.I.  相似文献   

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