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1.
Let and be C*-dynamical systems and assume that is a separable simple C*-algebra and that α and β are *-automorphisms. Then the semicrossed products and are isometrically isomorphic if and only if the dynamical systems and are outer conjugate.
K. R. Davidson was partially supported by an NSERC grant. E. G. Katsoulis was partially supported by a summer grant from ECU 相似文献
2.
We consider the computation of stable approximations to the exact solution of nonlinear ill-posed inverse problems F(x) = y with nonlinear operators F : X → Y between two Hilbert spaces X and Y by the Newton type methods
in the case that only available data is a noise of y satisfying with a given small noise level . We terminate the iteration by the discrepancy principle in which the stopping index is determined as the first integer such that
with a given number τ > 1. Under certain conditions on {α
k
}, {g
α
} and F, we prove that converges to as and establish various order optimal convergence rate results. It is remarkable that we even can show the order optimality
under merely the Lipschitz condition on the Fréchet derivative F′ of F if is smooth enough. 相似文献
3.
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
4.
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
5.
Concettina Galati 《Annali di Matematica Pura ed Applicata》2009,188(2):359-368
Let be the variety of irreducible sextics with six cusps as singularities. Let be one of irreducible components of . Denoting by the space of moduli of smooth curves of genus 4, we consider the rational map sending the general point [Γ] of Σ, corresponding to a plane curve , to the point of parametrizing the normalization curve of Γ. The number of moduli of Σ is, by definition the dimension of Π(Σ). We know that
, where ρ(2, 4, 6) is the Brill–Noether number of linear series of dimension 2 and degree 6 on a curve of genus 4. We prove that both
irreducible components of have number of moduli equal to seven.
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6.
Greg Friedman 《Mathematische Annalen》2009,343(2):371-395
Cohen, Goresky, and Ji showed that there is a Künneth theorem relating the intersection homology groups to and , provided that the perversity satisfies rather strict conditions. We consider biperversities and prove that there is a Künneth theorem relating to and for all choices of and . Furthermore, we prove that the Künneth theorem still holds when the biperversity p, q is “loosened” a little, and using this we recover the Künneth theorem of Cohen–Goresky–Ji. 相似文献
7.
Haïkel Skhiri 《Integral Equations and Operator Theory》2008,62(1):137-148
Let be the algebra of all bounded linear operators on a complex Banach space X and γ(T) be the reduced minimum modulus of operator . In this work, we prove that if , is a surjective linear map such that is an invertible operator, then , for every , if and only if, either there exist two bijective isometries and such that for every , or there exist two bijective isometries and such that for every . This generalizes for a Banach space the Mbekhta’s theorem [12].
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8.
J. Ruppenthal 《Mathematische Zeitschrift》2009,263(2):447-472
Let X be a regular irreducible variety in , Y the associated homogeneous variety in , and N the restriction of the universal bundle of to X. In the present paper, we compute the obstructions to solving the -equation in the L
p
-sense on Y for 1 ≤ p ≤ ∞ in terms of cohomology groups . That allows to identify obstructions explicitly if X is specified more precisely, for example if it is equivalent to or an elliptic curve.
相似文献
9.
Every skew Boolean algebra S has a maximal generalized Boolean algebra image given by S/ where is the Green’s relation defined initially on semigroups. In this paper we study skew Boolean algebras constructed from generalized Boolean algebras B by a twisted product construction for which . In particular we study the congruence lattice of with an eye to viewing as a minimal skew Boolean cover of B. This construction is the object part of a functor from the category GB of generalized Boolean algebras to the category LSB of left-handed skew Boolean algebras. Thus we also look at its left adjoint functor .
This paper was written while the second author was a Visiting Professor in the Department of Education at the University of
Cagliari. The facilities and assistance provided by the University and by the Department are gratefully acknowledged. 相似文献
10.
J. S. Manhas 《Integral Equations and Operator Theory》2008,62(3):419-428
Let be the weighted Banach space of analytic functions with a topology generated by weighted sup-norm. In the present article,
we investigate the analytic mappings and which characterize the compactness of differences of two weighted composition operators on the space . As a consequence we characterize the compactness of differences of composition operators on weighted Bloch spaces.
相似文献
11.
Let G be a connected graph. For at distance 2, we define , and , if then . G is quasi-claw-free if it satisfies , and G is P
3-dominated() if it satisfies , for every pair (x, y) of vertices at distance 2. Certainly contains as a subclass. In this paper, we prove that the circumference of a 2-connected P
3-dominated graph G on n vertices is at least min or , moreover if then G is hamiltonian or , where is a class of 2-connected nonhamiltonian graphs. 相似文献
12.
Nikolaos Bournaveas Hua Wang 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(1):131-142
We show how the methods of [6–8] can be used to prove velocity averaging lemmas in hyperbolic Sobolev spaces for the kinetic
transport equation . Here v is allowed to vary in the whole space and the velocity field lies on the unit sphere. We work in dimensions and, in contrast with [6, 8], we allow right-hand sides with velocity derivatives in any direction and not necessarily tangential
to the sphere.
相似文献
13.
Gelu Popescu 《Mathematische Annalen》2008,342(1):1-30
In this paper we obtain a noncommutative multivariable analogue of the classical Nevanlinna–Pick interpolation problem for
analytic functions with positive real parts on the open unit disc. Given a function , where is an arbitrary subset of the open unit ball , we find necessary and sufficient conditions for the existence of a free holomorphic function g with complex coefficients on the noncommutative open unit ball such that
where is the algebra of all bounded linear operators on a Hilbert space . The proof employs several results from noncommutative multivariable operator theory and a noncommutative Cayley transform
(introduced and studied in the present paper) acting from the set of all free holomorphic functions with positive real parts
to the set of all bounded free holomorphic functions. All the results of this paper are obtained in the more general setting
of free holomorphic functions with operator-valued coefficients. As consequences, we deduce some results concerning operator-valued
analytic interpolation on the unit ball .
Research supported in part by an NSF grant. 相似文献
14.
Peter L. Søndergaard 《Advances in Computational Mathematics》2007,27(4):355-373
By sampling the window of a Gabor frame for belonging to Feichtinger’s algebra, , one obtains a Gabor frame for . In this article we present a survey of results by R. Orr and A.J.E.M. Janssen and extend their ideas to cover interrelations
among Gabor frames for the four spaces , , and . Some new results about general dual windows with respect to sampling and periodization are presented as well. This theory
is used to show a new result of the Kaiblinger type to construct an approximation to the canonical dual window of a Gabor
frame for .
相似文献
15.
In this article we extend Milnor’s fibration theorem to the case of functions of the form with f, g holomorphic, defined on a complex analytic (possibly singular) germ (X, 0). We further refine this fibration theorem by looking not only at the link of , but also at its multi-link structure, which is more subtle. We mostly focus on the case when X has complex dimension two. Our main result (Theorem 4.4) gives in this case the equivalence of the following three statements:
Moreover one has that if these conditions hold, then the Milnor-Lê fibration of is a fibration of the multilink . We also give a combinatorial criterium to decide whether or not the multilink is fibered. If the meromorphic germ f/g is semitame, then we show that the Milnor-Lê fibration given by is equivalent to the usual Milnor fibration given by . We finish this article by discussing several realization problems.
Research partially supported by CONACYT and DGAPA-UNAM, Mexico, and by CNRS and ECOS, France. 相似文献
(i) | The real analytic germ has 0 as an isolated critical value; |
(ii) | the multilink is fibered; and |
(iii) | if is a resolution of the holomorphic germ , then for each rupture vertex (j) of the decorated dual graph of π one has that the corresponding multiplicities of f, g satisfy: . |
16.
Let be a field, and M and N two finitely generated graded modules over standard graded -algebras A and B, respectively. We will study generalized, sequentially, almost, and approximately Cohen–Macaulay as well as clean, and pretty
clean properties of the -module through the corresponding properties of M and N. The behavior of these properties with respect to the simplicial join of two simplicial (multi)complexes will be revealed
as corollaries. 相似文献
17.
Let be a finitely generated group and X its Cayley graph with respect to a finite, symmetric generating set S. Furthermore, let be a finite group and the lamplighter group (wreath product) over with group of “lamps” . We show that the spectral measure (Plancherel measure) of any symmetric “switch–walk–switch” random walk on coincides with the expected spectral measure (integrated density of states) of the random walk with absorbing boundary on
the cluster of the group identity for Bernoulli site percolation on X with parameter . The return probabilities of the lamplighter random walk coincide with the expected (annealed) return probabilities on the
percolation cluster. In particular, if the clusters of percolation with parameter are almost surely finite then the spectrum of the lamplighter group is pure point. This generalizes results of Grigorchuk
and Żuk, resp. Dicks and Schick regarding the case when is infinite cyclic. Analogous results relate bond percolation with another lamplighter random walk. In general, the integrated
density of states of site (or bond) percolation with arbitrary parameter is always related with the Plancherel measure of a convolution operator by a signed measure on , where or another suitable group.
M. Neuhauser’s research supported by the Marie-Curie Excellence Grant MEXT-CT-2004-517154.
The research of W. Woess was partially supported by Austrian Science Fund (FWF) P18703-N18. 相似文献
18.
Margherita Guida 《Ricerche di matematica》2008,57(1):159-167
In this paper we study the syzygy modules of a grid or a fat grid of . We compute the minimal free resolution for the ideal of a complete grid in , and we conjecture this resolution in . Moreover we compute the minimal free resolution for the ideal of an incomplete grid of . We also conjecture the minimal free resolution for the ideal of a fat complete grid in .
相似文献
19.
Christoph Barbian 《Integral Equations and Operator Theory》2008,61(3):299-323
By Beurling’s theorem, the orthogonal projection onto an invariant subspace M of the Hardy space on the unit disk can be represented as where Φ is an inner multiplier of . This concept can be carried over to arbitrary Nevanlinna-Pick spaces but fails in more general settings. This paper introduces
the notion of Beurling decomposable subspaces. An invariant subspace M of a reproducing kernel Hilbert space will be called Beurling decomposable if there exist (operator-valued) multipliers such that and . We characterize the finite-codimensional and the finite-rank Beurling decomposable subspaces by means of their core function
and core operator. As an application, we show that in many analytic Hilbert modules , every finite-codimensional submodule M can be written as with suitable polynomials p
i
.
相似文献
20.
Thomas Eckl 《Geometriae Dedicata》2008,137(1):149-162
Using Dumnicki’s approach to showing non-specialty of linear systems consisting of plane curves with prescribed multiplicities
in sufficiently general points on we develop an asymptotic method to determine lower bounds for Seshadri constants of general points on . With this method we prove the lower bound for 10 general points on .
相似文献