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871.
Ronald G.?DouglasEmail author Gadadhar?Misra 《Integral Equations and Operator Theory》2003,47(4):435-456
The notion of a quasi-free Hilbert module over a function algebra
$\mathcal{A}$ consisting of holomorphic functions on a bounded domain $\Omega$ in complex m
space is introduced. It is shown that quasi-free Hilbert modules correspond to
the completion of the direct sum of a certain number of copies of the algebra
$\mathcal{A}$. A Hilbert module is said to be weakly regular (respectively, regular) if there
exists a module map from a quasi-free module with dense range (respectively,
onto). A Hilbert module $\mathcal{M}$ is said to be compactly supported if there exists a
constant $\beta$ satisfying $\|\varphi f\| \leq \beta \ |\varphi \| \textsl{X} \|f \|$ for some compact subset X of $\Omega$ and
$\varphi$ in $\mathcal{A}$, f in $\mathcal{M}$. It is shown that if a Hilbert module is compactly supported
then it is weakly regular. The paper identifies several other classes of Hilbert
modules which are weakly regular. In addition, this result is extended to yield
topologically exact resolutions of such modules by quasi-free ones. 相似文献
872.
We introduce a class of function algebras, that we call unimodular,
and study Toeplitz operators on the Hardy spaces associated to representing
measures on these algebras.We show that our class of function algebras is very
extensive and that a number of important results for Toeplitz operators and
their associated C*-algebras extend to the very general setting we consider.
Submitted: July 1. 2001. 相似文献
873.
Valentina?CasarinoEmail author Klaus-Jochen?Engel Rainer?Nagel Gregor?Nickel 《Integral Equations and Operator Theory》2003,47(3):289-306
In this paper we convert a (linear abstract) initial boundary value
problem into an abstract Cauchy problem on some product space and use
semigroup methods to solve it. In particular, we apply spectral theory in
order to discuss stability under boundary feedback. 相似文献
874.
Given an admissible measure μ on where is an open set, we define a realization of the Laplacian in with general Robin boundary conditions and we show that generates a holomorphic C
0
-semigroup on which is sandwiched by the Dirichlet Laplacian and the Neumann Laplacian semigroups. Moreover, under a locality and a regularity
assumption, the generator of each sandwiched semigroup is of the form . We also show that if contains smooth functions, then μ is of the form (where σ is the (n-1)-dimensional Hausdorff measure and β a positive measurable bounded function on ); i.e. we have the classical Robin boundary conditions.
RID="h1"
ID="h1"Dédié à Philippe Bénilan
RID="*"
ID="h1"This work is part of the DGF-Project: "Regularit?t und Asymptotik für elliptische und parabolische Probleme". 相似文献
875.
876.
M. Chahboun A. El Kinani M. Oudadess 《Rendiconti del Circolo Matematico di Palermo》2001,50(2):271-284
We examine the structure and the spectral properties of locally uniformlyA-pseudo-convex algebras.
相似文献
877.
M. I. Ganzburg 《Constructive Approximation》2001,17(2):275-306
We study Pólya-and Remez-type inequalities for univariate and multivariate polynomials and discuss their applications to Nikolskii-type
inequalities and upper estimates of trigonometric integrals. 相似文献
878.
It is shown that the m th-order derivative of the n th-order Bernstein polynomial of a function f satisfying a certain Lipschitz condition, can be written for n\rightarrow +∈fty as a singular integral of Gauss—Weierstrass type, m times differentiated (in a certain sense) under the integral sign. The theorem is applied to yield an overdifferentiation formula, involving p times differentiated Bernstein polynomials of functions that are not C
p
.
December 1, 1998. Dates revised: July 22, 1999 and January 11, 2000. Date accepted: February 1, 2000. 相似文献
879.
Roger Nussbaum 《Integral Equations and Operator Theory》2001,39(1):41-97
LetC(S) denote the Banach space of continuous, real-valued mapsf:S and letA denote a positive linear map ofC(S) into itself. We give necessary conditions that the operatorA have a strictly positive periodic point of minimal periodm. Under mild compactness conditions on the operatorA, we prove that these necessary conditions are also sufficient to guarantee existence of a strictly positive periodic point of minimal periodm. We study a class of Perron-Frobenius operators defined by
and we show how to verify the necessary compactness conditions to apply our theorems concerning existence of positive periodic points.Partially supported by NSF DMS 97-06891 相似文献
880.
In this paper we introduce a class of operators naturally extending the classes of hyponormal and posinormal operators. For this class we construct a generating family of eigendistributions, unitary invariants and a functional model. 相似文献