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1.
The purpose of this paper is to give characterizations for uniform exponential dichotomy of evolution families on the real
line. We consider a general class of Banach function spaces denoted
and we prove that if
with
and the pair
is admissible for an evolution family
then
is uniformly exponentially dichotomic. By an example we show that the admissibility of the pair
for an evolution family is not a sufficient condition for uniform exponential dichotomy. As applications, we deduce necessary
and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pairs
and
with
相似文献
2.
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
|
3.
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
4.
Given real numbers
with 00 >0 , the truncated parabolic moment problem for entails finding necessary and sufficient conditions for the existence of a positive Borel measure , supported in the parabola p(x, y) = 0, such that
We prove that admits a representing measure (as above) if and only if the associated moment matrix
is positive semidefinite, recursively generated and has a column relation p(X, Y) = 0, and the algebraic variety () associated to satisfies card
In this case, admits a rank
-atomic (minimal) representing measure.Submitted: August 25, 2003 相似文献
5.
6.
The purpose of this paper is to give new and general characterizations for uniform dichotomy and uniform exponential dichotomy
of evolution families on the real line. We consider two general classes denoted
and
and we prove that if V,W are Banach function spaces with
and
, then the admissibility of the pair
for an evolution family
implies the uniform dichotomy of
. In addition, we consider a subclass
and we prove that if
, then the admissibility of the pair
implies the uniform exponential dichotomy of the family
. This condition becomes necessary if
. Finally, we present some applications of the main results. 相似文献
7.
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
8.
9.
10.
M. Laczkovich 《Aequationes Mathematicae》2004,68(3):177-199
11.
V. A. Kucher X. Markenscoff 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(6):1065-1073
The Cosserat eigenvalue problem for the elliptic exterior is considered. It is shown that the only Cosserat eigenvalue different from the infinite multiple eigenvalues
and
is
which also has an infinite multiplicity. The orthogonal basis of the eigenspace corresponding to
is constructed. Application to thermoelasticity and Stokes flow – extensional and shear – past a rigid elliptical cylinder are presented and agreement is obtained with classical solutions for a circle. The fact that the solutions consist of only two eigenfunctions reveals the efficiency of the method.Received: February 27, 2003 相似文献
12.
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
13.
Albert Wiltsche 《Journal of Geometry》2008,88(1-2):178-193
We discuss all automorphisms of which have a space cubic (twisted cubic) as a fixed figure. These automorphisms build up a three-parameter subgroup of all collineations of . In this paper we study the one-parameter subgroups of , their paths and tangent complexes.
相似文献
14.
Hidetoshi Maeda 《Archiv der Mathematik》2007,88(5):419-424
Let
be an ample vector bundle of rank n – 1 on a smooth complex projective variety X of dimension n≥ 3 such that X is a
-bundle over
and that
for any fiber F of the bundle projection
. The pairs
with
= 2 are classified, where
is the curve genus of
. This allows us to improve some previous results.
Received: 13 June 2006 相似文献
15.
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)) |
16.
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
17.
Christian Dzierzon 《Applied Categorical Structures》2006,14(1):63-80
This paper presents a general construction, defining for each given strong generator in any locally finitely presentable category an essentially algebraic, finitary theory – maximal in a certain sense – such that is equivalent to the category of models of . For regular generators , generalization to the non-finitary case is easily done, and yields a new proof of the famous characterization of many-sorted
quasivarieties. 相似文献
18.
This paper is concerned with the linear signal response analysis of a thin viscous liquid sheet which is at rest in an appropriate frame of reference and in contact with passive external media, and on which localized external pressures act from the passive media as sources of perturbation.The frame of the analysis is provided by general formulae for the response signals of the sheet in the two excitation modes, sinuous and varicose, which result as the solution of the appropriate fluid dynamic initial-boundary value problems by the Fourier-Laplace transform technique. These formulae display how the signals depend on the nature of the perturbation and on the spectrum of the (linear) eigenmodes of the sheet.The signals can be evaluated either numerically or, as initiated in this paper, analytically, in long wave approximations. The long wave approximation will be seen in the sequel to concentrate on particular eigenmodes of the sheet spectrum, with small values k of the wave vector
along the sheet. The present paper is devoted mainly to a detailed analysis of the spectrum of eigenmodes of the sheet, and to the formulation of long wave approximations of (linear) response signals of the sheet in the context of this analysis.It turns out that the sheet spectrum of eigenmodes depends on only one characteristic number , which depends on the (positive) fluid parameters: the surface tension at (both) the interfaces of the sheet, the density of the fluid, its kinematic viscosity , and on the thickness h of the sheet:
This number is closely related, by
to the Ohnesorge number
where
is the dynamic viscosity of the liquid.It will be shown in the sequel that of the infinitely many branches of the sheet spectrum only two (pairs of) soft branches, one sinuous and one varicose, will be relevant for a long wave approximation. For these branches asymptotic expansions of the dispersion relations (k) between the (complex) mode frequencies and
for long waves (i.e. for k 0), which obey (k) 0 with k 0, will be derived.The analytic long wave dispersion relations for the (soft) sinuous and varicose spectral branches allow a very favourable insight into the qualitative mode behaviour, including analogies beyond liquid sheets. They show e.g. that to their lowest orders in k the soft sinuous modes are nondispersive, i.e.
and only weakly absorptive, i.e. k2 for low viscosity and k4 for high viscosity ( < 0). Their signals are therefore expected to have some resemblance to signals of a flexible membrane on the one side and those of a (2-dimensional) diffusion process, or a hyperdiffusion process where
is replaced by
The behaviour of the soft varicose modes will be seen to depend on the value of : For 2 < 4 the asymptotic expansion for k 0 gives
and k2( < 0), i.e. the modes are purely absorptive, like those of (ordinary) diffusion processes. For 2 > 4 the situation is different: here
and k2 ( < 0). This behaviour bears resemblance to the vibration modes of a thin elastic plate with (diffusion-like) damping.The asymptotic insight into the behaviour of the individual branches of spectral modes allows the derivation of rather transparent approximate analytic expressions for the response signals of the sheet to external perturbations.Received: August 11, 2003; revised: August 10, 2004 相似文献
19.
Federico Ardila 《Annals of Combinatorics》2005,8(4):379-389
Given a matroid M on the ground set E, the Bergman fan
or space of M-ultrametrics, is a polyhedral complex in
which arises in several different areas, such as tropical algebraic geometry, dynamical systems, and phylogenetics. Motivated by the phylogenetic situation, we study the following problem: Given a point in
we wish to find an M-ultrametric which is closest to it in the
-metric. The solution to this problem follows easily from the existence of the subdominant M-ultrametric: a componentwise maximum M-ultrametric which is componentwise smaller than . A procedure for computing it is given, which brings together the points of view of matroid theory and tropical geometry. When the matroid in question is the graphical matroid of the complete graph Kn, the Bergman fan
parameterizes the equidistant phylogenetic trees with n leaves. In this case, our results provide a conceptual explanation for Chepoi and Fichets method for computing the tree that most closely matches measured data.Received August 12, 2004 相似文献
20.
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