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1.
We consider Hilbert spaces
of analytic functions defined on an open subset
of
, stable under the operator Mu of multiplication by some function u. Given a subspace
of
which is nearly invariant under division by u, we provide a factorization linking each element of
to elements of
on the inverse image under u of a certain complex disc, for which we give a relatively simple formula. By applying these results to
and u(z) = z, we obtain interesting results involving a H2-norm control. In particular, we deduce a factorization for the kernel of Toeplitz operators on Dirichlet spaces. Finally, we give a localization for the problem of extraneous zeros.Submitted: January 18, 2003 Revised: December 20, 2003 相似文献
2.
The Aronszajn–Donoghue Theory for Rank One Perturbations of the
$$\mathcal{H}_{-2} {\text{-Class}}$$
A singular rank one perturbation
of a self-adjoint operator A in a Hilbert space
is considered, where
and
but
with
the usual A–scale of Hilbert spaces. A modified version of the Aronszajn-Krein formula is given. It has the form
where F denotes the regularized Borel transform of the scalar spectral measure of A associated with . Using this formula we develop a variant of the well known Aronszajn–Donoghue spectral theory for a general rank one perturbation of the
class.Submitted: March 14, 2002 Revised: December 15, 2002 相似文献
3.
In this paper, we give an Lp-Lq-version of Morgans theorem for the Dunkl-Bessel transform
on
More precisely, we prove that for all
and
then for all measurable function f on
the conditions
and
imply f = 0, if and only if
where
are the Lebesgue spaces associated with the Dunkl-Bessel transform.Received: November 21, 2003 Revised: April 26, 2004 Accepted: May 28, 2004 相似文献
4.
Raúl E. Curto Lawrence A. Fialkow H. Michael Möller 《Integral Equations and Operator Theory》2008,60(2):177-200
For a degree 2n real d-dimensional multisequence to have a representing measure μ, it is necessary for the associated moment matrix to be positive semidefinite and for the algebraic variety associated to β, , to satisfy rank card as well as the following consistency condition: if a polynomial vanishes on , then . We prove that for the extremal case , positivity of and consistency are sufficient for the existence of a (unique, rank -atomic) representing measure. We also show that in the preceding result, consistency cannot always be replaced by recursiveness
of .
The first-named author’s research was partially supported by NSF Research Grants DMS-0099357 and DMS-0400741. The second-named
author’s research was partially supported by NSF Research Grant DMS-0201430 and DMS-0457138. 相似文献
5.
In this paper, we consider global solutions for the following nonlinear Schrödinger equation
in
with
and
We show that no nontrivial solution can decay faster than the solutions of the free Schrödinger equation, provided that u(0) lies in the weighted Sobolev space
in the energy space, namely
or in
according to the different cases. 相似文献
6.
For a class of essentially normal operators, we characterize their norm closures of
–orbits. Moreover, we introduce a notion of the quasiapproximate
– equivalence of essentially normal operators and determine completely the quasiapproximate
–invariants. Finally, we give the canonical forms of essentially normal operators under this quasiapproximate
–equivalence. 相似文献
7.
Scott McCullough 《Integral Equations and Operator Theory》2001,39(3):335-362
Let
denote an annulus,E a finite subset of
with at least three elements, and
the ideal of functions in
which vanish at the points ofE. The quotient
does not have a completely isometric representation on a finite dimensional Hilbert space. This complements a result of [11] which implies that the quotient has an isometric representation on a Hilbert space of dimension twice the cardinality ofE. 相似文献
8.
The aim of this paper is to give necessary and sufficient conditions for pointwise and uniform exponential dichotomy of linear skew-product flows. We shall obtain that the pointwise exponential dichotomy of a linear skew-product flow is equivalent to the pointwise admissibility of the pair
As a consequence, we prove that a linear skew-product flow on
is uniformly exponentially dichotomic if and only if the pair
is uniformly admissible for . 相似文献
9.
Suppose A generates a strongly continuous linear group
on a Banach space X and B is a linear operator on X. It is shown that an extension of
generates a strongly continuous semigroup if and only if the family of operators
has an appropriate evolution system. This produces simple sufficient conditions for an extension of
to generate a strongly continuous semigroup, including
相似文献
(1) | being m-dissipative and for all x in the domain of B; or | ||
(2) |
being m-dissipative and
being a commuting family of operators with
|
10.
11.
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
12.
13.
We examine the operator algebra
behind the boundary integral equation method for solving transmission problems. A new type of boundary integral operator, the rotation operator, is introduced, which is more appropriate than operators of double layer type for solving transmission problems for first order elliptic partial differential equations. We give a general invertibility criteria for operators in
by defining a Clifford algebra valued Gelfand transform on
. The general theory is applied to transmission problems with strongly Lipschitz interfaces for the two classical elliptic operators
and . We here use Rellich techniques in a new way to estimate the full complex spectrum of the boundary integral operators. For
we use the associated rotation operator to solve the Hilbert boundary value problem and a Riemann type transmission problem. For the Helmholtz equation, we demonstrate how Rellich estimates give an angular spectral estimate on the rotation operator, which with the general spectral mapping properties in
translates to a hyperbolic spectral estimate for the double layer potential operator. 相似文献
14.
On the atomic conditions of lattice-ordered groups 总被引:2,自引:0,他引:2
We introduce large convex
-subgroups to study the structure of the lattice-ordered groups
G whose C(G), P(G) and (G) satisfy atomic conditions, where C(G), P(G) and (G) denote respectively the lattice of all convex
-subgroups, the lattice of all polar subgroups and the root system of all regular subgroups of G. In particular, we construct a new torsion class
defined as the class of
-groups G for which all large prime subgroups are maximal. We prove that the class of hyperarchimedean
-groups is properly contained within
and that any
-group within
has the property that any chain of prime subgroups has length at most 2.Received October 7, 2003; accepted in final form June 11, 2004. 相似文献
15.
On the Range of the Aluthge Transform 总被引:1,自引:0,他引:1
Let
be the algebra of all bounded linear operators on a complex separable Hilbert space
For an operator
let
be the Aluthge transform of T and we define
for all
where T = U|T| is a polar decomposition of T. In this short note, we consider an elementary property of the range
of Δ. We prove that R(Δ) is neither closed nor dense in
However R(Δ) is strongly dense if
is infinite dimensional.
An erratum to this article is available at . 相似文献
16.
In the case of radial symbols we study the behavior of different properties (boundedness, compactness, spectral properties, etc.) of Toeplitz operators Ta() acting on weighted Bergman spaces
over the unit disk
, in dependence on , and compare their limit behavior under
with corresponding properties of the initial symbol a. 相似文献
17.
M. Laczkovich 《Aequationes Mathematicae》2004,68(3):177-199
18.
Let Q(x, y) = 0 be an hyperbola in the plane. Given real numbers β ≡ β (2n)={ β ij } i,j ≥ 0,i+j ≤ 2n , with β00 > 0, the truncated Q-hyperbolic moment problem for β entails finding necessary and sufficient conditions for the existence of a positive Borel measure μ, supported in Q(x, y) = 0, such that
We prove that β admits a Q-representing measure μ (as above) if and only if the associated moment matrix
is positive semidefinite, recursively generated, has a column relation Q(X,Y) = 0, and the algebraic variety
associated to β satisfies card
In this case,
if
then β admits a rank
-atomic (minimal) Q-representing measure; if
then β admits a Q-representing measure μ satisfying
相似文献
19.
Dietmar Vogt 《Archiv der Mathematik》2006,87(2):163-171
It is shown that for open convex
, d > 1 and a nontrivial polynomial P the space
does not have property
. If P is elliptic or homogeneous, then this holds for every open Ω. For
even
cannot occur and if it occurs for some Ω, then P must be hypoelliptic.
Received: 18 July 2005 相似文献
20.
We consider parabolic variational inequalities having the strong formulation
where
for some admissible initial datum, V is a separable Banach space with separable dual
is an appropriate monotone operator, and
is a convex,
lower semicontinuous functional. Well-posedness of (1) follows from an explicit construction of the related semigroup
Illustrative applications to free boundary problems and to parabolic problems in Orlicz-Sobolev spaces are given. 相似文献
((1)) |