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1.
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)) |
2.
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
3.
4.
For a convex body
in
which is invariant under rotations around one coordinate axis and has a smooth boundary of bounded nonzero curvature, the lattice point discrepancy
(number of integer points minus volume) of a linearly dilated copy
is estimated from below. On the basis of a recent method of K. Soundararajan [16], an -bound is obtained that improves upon all earlier results of this kind.Dedicated to the memory of Professor Erich LamprechtThis revised electronic version of the Abstract includes the formulas that were missing in the previous electronic version published online in September 2004. 相似文献
5.
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
|
6.
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
7.
M. Laczkovich 《Aequationes Mathematicae》2004,68(3):177-199
8.
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
9.
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
10.
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