共查询到20条相似文献,搜索用时 31 毫秒
1.
Ameer Athavale 《Complex Analysis and Operator Theory》2008,2(3):417-428
Let be a strictly pseudoconvex bounded domain in with C
2 boundary . If a subnormal m-tuple T of Hilbert space operators has the spectral measure of its minimal normal extension N supported on , then T is referred to as a -isometry. Using some non-trivial approximation theorems in the theory of several complex variables, we establish a commutant
lifting theorem for those -isometries whose (joint) Taylor spectra are contained in a special superdomain Ω of . Further, we provide a function-theoretic characterization of those subnormal tuples whose Taylor spectra are contained in
Ω and that are quasisimilar to a certain (fixed) -isometry T (of which the multiplication tuple on the Hardy space of the unit ball in is a rather special example).
Submitted: September 9, 2007. Revised: October 10, 2007. Accepted: October 24, 2007. 相似文献
2.
Thomas Krainer 《Annals of Global Analysis and Geometry》2009,35(4):345-361
Let A be an elliptic operator on a compact manifold with boundary , and let be a covering map, where Y is a closed manifold. Let A
C
be a realization of A subject to a coupling condition C that is elliptic with parameter in the sector Λ. By a coupling condition we mean a nonlocal boundary condition that respects
the covering structure of the boundary. We prove that the resolvent trace for N sufficiently large has a complete asymptotic expansion as . In particular, the heat trace has a complete asymptotic expansion as , and the -function has a meromorphic extension to .
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3.
We present a new distance characterization of Aleksandrov spaces of non-positive curvature. By introducing a quasilinearization
for abstract metric spaces we draw an analogy between characterization of Aleksandrov spaces and inner product spaces; the
quasi-inner product is defined by means of the quadrilateral cosine—a metric substitute for the angular measure between two
directions at different points. Our main result states that a geodesically connected metric space is an Aleksandrov domain (also known as a CAT(0) space) if and only if the quadrilateral cosine does not exceed one for every two pairs of
distinct points in . We also observe that a geodesically connected metric space is an domain if and only if, for every quadruple of points in , the quadrilateral inequality (known as Euler’s inequality in ) holds. As a corollary of our main result we give necessary and sufficient conditions for a semimetric space to be an domain. Our results provide a complete solution to the Curvature Problem posed by Gromov in the context of metric spaces
of non-positive curvature.
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4.
Let be a saturated formation. We describe minimal non- -, minimal non- -, and minimal non-metabelian groups.
Dedicated to L. A. Shemetkov on the occasion of his seventieth birthday. 相似文献
5.
Bounded universal functions in one and several complex variables 总被引:2,自引:0,他引:2
We show how to obtain functions that are universal for the ball of , where . The existence of our functions will follow from universality criteria, but we also show how to construct them. Then we study
the connection between certain interpolating sequences, runaway automorphisms, and the existence of universal functions on
domains in .
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6.
7.
Valentina S. Harizanov Carl G. JockuschJr. Julia F. Knight 《Archive for Mathematical Logic》2009,48(1):39-53
We study the complexity of infinite chains and antichains in computable partial orderings. We show that there is a computable
partial ordering which has an infinite chain but none that is or , and also obtain the analogous result for antichains. On the other hand, we show that every computable partial ordering
which has an infinite chain must have an infinite chain that is the difference of two sets. Our main result is that there is a computably axiomatizable theory K of partial orderings such that K has a computable model with arbitrarily long finite chains but no computable model with an infinite chain. We also prove
the corresponding result for antichains. Finally, we prove that if a computable partial ordering has the feature that for every , there is an infinite chain or antichain that is relative to , then we have uniform dichotomy: either for all copies of , there is an infinite chain that is relative to , or for all copies of , there is an infinite antichain that is relative to . 相似文献
8.
Ian Chiswell Thomas W. Müller Jan-Christoph Schlage-Puchta 《Archiv der Mathematik》2008,91(4):372-378
We establish (geometric) criteria for an -tree to be compact and to be locally compact. It follows that locally compact -trees are separable.
Received: 10 September 2007 相似文献
9.
Pairs of numerically satisfactory solutions as for the three-term recurrence relations satisfied by the families of functions , , are given. It is proved that minimal solutions always exist, except when and z is in the positive or negative real axis, and that is minimal as whenever . The minimal solution is identified for any recurrence direction, that is, for any integer values of and . When the confluent limit , with fixed, is the main tool for identifying minimal solutions together with a connection formula; for , is the main tool to be considered. 相似文献
10.
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
11.
Elena I. Kaikina Leonardo Guardado-Zavala Hector F. Ruiz-Paredes Jesus A. Mendez Navarro 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(1):63-77
We study nonlinear nonlocal equations on a half-line in the critical case
where . The linear operator is a pseudodifferential operator defined by the inverse Laplace transform with dissipative symbol , the number . The aim of this paper is to prove the global existence of solutions to the inital-boundary value problem (0.1) and to find
the main term of the large time asymptotic representation of solutions in the critical case.
相似文献
12.
Álvaro Lozano-Robledo 《manuscripta mathematica》2008,126(3):393-407
Let S be an infinite set of rational primes and, for some p ∈ S, let be the compositum of all extensions unramified outside S of the form , for . If , let be the intersection of the fixed fields by , for i = 1, . . , n. We provide a wide family of elliptic curves such that the rank of is infinite for all n ≥ 0 and all , subject to the parity conjecture. Similarly, let be a polarized abelian variety, let K be a quadratic number field fixed by , let S be an infinite set of primes of and let be the maximal abelian p-elementary extension of K unramified outside primes of K lying over S and dihedral over . We show that, under certain hypotheses, the -corank of sel
p
∞(A/F) is unbounded over finite extensions F/K contained in . As a consequence, we prove a strengthened version of a conjecture of M. Larsen in a large number of cases. 相似文献
13.
Michele Bolognesi 《Mathematische Zeitschrift》2009,261(1):149-168
Let C be a genus 2 curve and the moduli space of semi-stable rank 2 vector bundles on C with trivial determinant. In Bolognesi (Adv Geom 7(1):113–144, 2007) we described the parameter space of non stable extension
classes of the canonical sheaf ω of C by ω−1. In this paper, we study the classifying rational map that sends an extension class to the corresponding rank two vector bundle. Moreover, we prove that, if we blow up along a certain cubic surface S and at the point p corresponding to the bundle , then the induced morphism defines a conic bundle that degenerates on the blow up (at p) of the Kummer surface naturally contained in . Furthermore we construct the -bundle that contains the conic bundle and we discuss the stability and deformations of one of its components. 相似文献
14.
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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15.
Jean Bourgain 《Geometric And Functional Analysis》2009,18(5):1477-1502
The main result of this paper is an exponential sum bound in prime fields for multilinear expressions of the type under nearly optimal conditions on . It provides the expected generalization of the well-known inequality for r = 2. We also establish a new result on Gauss sums for multiplicative subgroups H of , obtaining a nontrivial estimate provided . This is a further improvement on [BGK].
Received: May 2007, Revision: October 2007, Accepted: October 2007 相似文献
16.
Euisung Park 《Mathematische Zeitschrift》2007,256(3):685-697
In this article we study nondegenerate projective curves of degree d which are not arithmetically Cohen-Macaulay. Note that for a rational normal curve and a point . Our main result is about the relation between the geometric properties of X and the position of P with respect to . We show that the graded Betti numbers of X are uniquely determined by the rank of P with respect to . In particular, X satisfies property N
2,p
if and only if . Therefore property N
2,p
of X is controlled by and conversely can be read off from the minimal free resolution of X. This result provides a non-linearly normal example for which the converse to Theorem 1.1 in (Eisenbud et al., Compositio
Math 141:1460–1478, 2005) holds. Also our result implies that for nondegenerate projective curves of degree d which are not arithmetically Cohen–Macaulay, there are exactly distinct Betti tables. 相似文献
17.
Nic Koban 《Geometriae Dedicata》2007,124(1):133-141
We compute the geometric invariants of a product G × H of groups in terms of and . This gives a sufficient condition in terms of and for a normal subgroup of G × H with abelian quotient to be of type F
n
. We give an example involving the direct product of the Baumslag–Solitar group BS1,2 with itself.
相似文献
18.
Nicola Garofalo 《manuscripta mathematica》2008,126(3):353-373
We prove some new a priori estimates for H
2-convex functions which are zero on the boundary of a bounded smooth domain Ω in a Carnot group . Such estimates are global and are geometric in nature as they involve the horizontal mean curvature of ∂Ω. As a consequence of our bounds we show that if has step two, then for any smooth H
2-convex function in vanishing on ∂Ω one has
.
Supported in part by NSF Grant DMS-07010001. 相似文献
19.
Pseudomonotone maps are a generalization of paramonotone maps which is very closely related to the cutting plane property in variational
inequality problems (VIP). In this paper, we first generalize the so-called minimum principle sufficiency and the maximum
principle sufficiency for VIP with multivalued maps. Then we show that pseudomonotonicity of the map implies the “maximum principle sufficiency” and, in fact, is equivalent to it in a sense. We then present two
applications of pseudomonotone maps. First we show that pseudomonotone maps can be used instead of the much more restricted class of pseudomonotone+ maps in a cutting plane method. Finally, an application to a proximal point method is given.
相似文献
20.
Jin Han Park Jong Seo Park Young Chel Kwun 《Fuzzy Optimization and Decision Making》2008,7(4):305-315
In this paper, we give some common fixed point theorems for five mappings satisfying some conditions in -fuzzy metric spaces. 相似文献