共查询到20条相似文献,搜索用时 15 毫秒
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Yucheng Li 《Integral Equations and Operator Theory》2009,63(1):95-102
Let D be the unit disk and be the weighted Bergman space. In this paper, we prove that the multiplication operator is similar to
M
z
on .
The author was supported in part by NSF Grant (10571041, L2007B05). 相似文献
4.
In this paper a trace functional is defined for the algebra of classical
anisotropic pseudo-differential operators on a compact foliated manifold.
Furthermore, by means of the Weyl formula, a formula is proved specifying
the link between this trace and Dixmier's trace.
Submitted: June 11, 2001?Revised: February 17, 2002 相似文献
5.
We explore the continuity of the map which, given an analytic selfmap
of the disk, takes as its value the norm of the associated composition
operator on the Hardy space . We also examine the continuity the functions
which assign to a self-map of the disk the Hilbert-Schmidt norm or the
essential norm of the associated composition operator and show these to be
discontinuous. Additionally, we characterize when the norm of a composition
operator is minimal.
Submitted: January 3, 2002? Revised: March 1, 2002. 相似文献
6.
《复变函数与椭圆型方程》2012,57(8):705-709
It is shown that the property of completeness of the Bergman metric of a planar domain whose complement is not a polar set, is a local one. 相似文献
7.
Carlos F. Borges 《Numerische Mathematik》1994,67(3):271-288
Summary. We consider a problem that arises in the evaluation of computer graphics
illumination models. In particular, there is a need to find a finite
set of wavelengths at which the illumination model should be evaluated.
The result of evaluating the illumination model at these points is a
sampled representation of the spectral power density of light emanating
from a point in the scene. These values are then used to determine the
RGB coordinates of the light by evaluating three definite integrals,
each with a common integrand (the SPD) and interval of integration but
with distinct weight functions. We develop a method for selecting the
sample wavelengths in an optimal manner.
More abstractly, we examine the problem of numerically evaluating a set
of definite integrals taken with respect to
distinct weight
functions but related by a common integrand and interval of integration.
It is shown that when it is not efficient
to use a set of
Gauss rules because valuable information is wasted. We go on to extend
the notions used in Gaussian quadrature to find an optimal set of
shared abcissas that maximize precision in a well-defined sense.
The classical Gauss rules come out as the special case
and some
analysis is given concerning the existence of these rules when
. In particular, we give conditions on the
weight functions that are
sufficient to guarantee that the shared abcissas are real, distinct, and
lie in the interval of integration. Finally, we examine some
computational strategies for constructing these rules.
Received July 15, 1991 相似文献
8.
N.L. Vasilevski 《Integral Equations and Operator Theory》2003,46(2):235-251
We exhibit a surprising but natural connection among the Bergman
space structure, commutative algebras of Toeplitz operators and pencils of
hyperbolic straight lines. The commutative C*-algebras of Toeplitz operators
on the unit disk can be classified as follows. Each pencil of hyperbolic straight
lines determines the set of symbols consisting of functions which are constant
on corresponding cycles, the orthogonal trajectories to lines forming a pencil.
It turns out that the C*-algebra generated by Toeplitz operators with this
class of symbols is commutative.
Submitted: January 15, 2001?Revised: February 7, 2002 相似文献
9.
Sherwin Kouchekian 《Integral Equations and Operator Theory》2003,45(3):319-342
The unbounded Bergman operator, the operator of multiplication
by on an unbounded open subset of the plane, is considered. We give a complete
answer regarding the density problem of unbounded Bergman operators
in terms of its equivalence to the problem of bounded point evaluations for the
Bergman spaces. Using this equivalence and the notion of Wiener capacity, we
obtain simple geometric conditions that classify almost those open subsets of
the plane for which the corresponding Bergman operators are densely defined.
With the aid of an analytic approach, we are also able to give condition for a
large collection of open subsets of the plane for which all the positive integer
powers of the corresponding Bergman operators are densely defined.
Submitted: December 14, 2001? Revised: January 14, 2001. 相似文献
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Kaisa Matomäki 《Monatshefte für Mathematik》2008,155(2):167-189
Let 1/5 < θ ≤ 1. We prove that there exists a positive constant δ such that the number of even integers in the interval [X, X + X
θ] which are not a sum of two primes is 《 X
θ−δ. The proof uses the circle method, a sieve method, exponential sum estimates and zero-density estimates for L-functions.
Current address: Department of Mathematics, 20014 University of Turku, Finland.
Author’s address: Department of Mathematics, University of London, Royal Holloway, Egham, Surrey TW20 0EX, UK 相似文献
12.
Summary. In the Dual-Primal FETI method, introduced by Farhat et al. [5], the domain is decomposed into non-overlapping subdomains,
but the degrees of freedom on crosspoints remain common to all subdomains adjacent to the crosspoint. The continuity of the
remaining degrees of freedom on subdomain interfaces is enforced by Lagrange multipliers and all degrees of freedom are eliminated.
The resulting dual problem is solved by preconditioned conjugate gradients. We give an algebraic bound on the condition number,
assuming only a single inequality in discrete norms, and use the algebraic bound to show that the condition number is bounded
by for both second and fourth order elliptic selfadjoint problems discretized by conforming finite elements, as well as for
a wide class of finite elements for the Reissner-Mindlin plate model.
Received January 20, 2000 / Revised version received April 25, 2000 / Published online December 19, 2000 相似文献
13.
Algebraic Properties of Toeplitz Operators with Radial Symbols on the Bergman Space of the Unit Ball
In this paper, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Bergman space of the
unit ball in . We first determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator. Next, we investigate
the zero-product problem for several Toeplitz operators with radial symbols. Also, the corresponding commuting problem of
Toeplitz operators whose symbols are of the form is studied, where and φ is a radial function.
Ze-Hua Zhou: supported in part by the National Natural Science Foundation of China (Grand Nos.10671141, 10371091). 相似文献
14.
The Iterated Aluthge Transform of an Operator 总被引:1,自引:0,他引:1
The Aluthge transform (defined below) of an operator T on
Hilbert space has been studied extensively, most often in connection with
p-hyponormal operators. In [6] the present authors initiated a study of various
relations between an arbitrary operator T and its associated , and this
study was continued in [7], in which relations between the spectral pictures
of T and were obtained. This article is a continuation of [6] and [7]. Here
we pursue the study of the sequence of Aluthge iterates {
(n)} associated
with an arbitrary operator T. In particular, we verify that in certain cases
the sequence {
(n)} converges to a normal operator, which partially answers
Conjecture 1.11 in [6] and its modified version below (Conjecture 5.6).
Submitted: December 5, 2000? Revised: August 30, 2001. 相似文献
15.
Giovanni Cimatti 《Annali di Matematica Pura ed Applicata》2002,181(2):181-212
The stability of the stationary solution of the thermistor as a circuit element is studied using a Liapunov functional and
the Hale–LaSalle invariance principle. The asymptotic stability of a class of periodic solutions is also considered.
Received: November 22, 1999; in final form: May 23, 2001?Published online: May 29, 2002 相似文献
16.
Liliana Pavel 《Mediterranean Journal of Mathematics》2008,5(3):341-356
Let K be a compact hypergroup.We investigate Trig(K), the linear span of coordinate functions of the irreducible representations of K. Contrary to the group case, Trig(K) endowed with the usual multiplication does not bear an algebra structure, but it has a natural normed algebra structure
when it inherits the convolution from , the algebra of all bounded Radon measures. We characterize the center of the algebras , L
p
(K) and Trig(K) respectively, and consequently we obtain, for a certain class of hypergroups, the correspondence between the structure space
of the center of L
1(K) and the center of Trig(K). As an application we study the existence of a finite universal Korovkin set w.r.t. positive operators in the center of
L
1(K), in particular in L
1(K), whenever K is commutative.
The author was partially supported by the Romanian Academy under the grant No. 22/2007. 相似文献
17.
W. E. Longstaff 《Integral Equations and Operator Theory》2003,45(3):343-350
In complex, separable, infinite-dimensional Hilbert space there exist
5 proper dense operator ranges with the property that every operator leaving
each of them invariant is a scalar multiple of the identity. The algebra of
operators leaving a pair of proper dense operator ranges invariant can have
an infinite nest of invariant subspaces. A slight extension of Foiaş' Theorem
shows that it can also have a non-trivial reducing subspace.
Submitted: July 13, 2001? Revised: December 6, 2001. 相似文献
18.
Let X be a Stein manifold. Then we prove that for any family ℱ⊂?(X) the normality domain Dℱ) is a meromorphically ?(X)-convex open set of X.
Received: 4 November 1999 相似文献
19.
Summary. We construct a quadrature formula for integration on the unit disc which is based on line integrals over distinct chords in the disc and integrates exactly all polynomials in two variables of total degree .
Received August 8, 1996 / Revised version received July 2, 1997 相似文献
20.
《复变函数与椭圆型方程》2012,57(12):845-850
In this paper, we express the essential norm of a composition operator on Bergman spaces of the unit ball in terms of an asymptotic upper bound of a quantity involving the pull-back measure induced by the inducing map. The result could be generalized to convex domains of finite type and to the weighted situation. 相似文献