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1.
Let X and Y be reflexive Banach spaces with strictly convexduals, and let T be a compact linear map from X to Y. It isshown that a certain nonlinear equation, involving T and itsadjoint, has a normalised solution (an eigenvector)corresponding to an eigenvalue, and that the sameis true for each member of a countable family of similar equationsinvolving the restrictions of T to certain subspaces of X. Theaction of T can be described in terms of these eigenvectors.There are applications to the p-Laplacian, the p-biharmonicoperator and integral operators of Hardy type. 相似文献
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In this paper we determine the possible Hilbert functions ofa CohenMacaulay local ring of dimension d and multiplicitye, in the case where the embedding dimension v satisfies v =e + d 3 and the CohenMacaulay type is less thanor equal to e 3. 1991 Mathematics Subject Classification:primary 13D40; secondary 13P99. 相似文献
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Let M be a Hamiltonian K-space with proper moment map µ.The symplectic quotient X = µ1(0)/K is a singularstratified space with a symplectic structure on the strata.In this paper we generalise the Kirwan map, which maps the Kequivariant cohomology of µ1(0) to the middle perversityintersection cohomology of X, to this symplectic setting. The key technical results which allow us to do this are Meinrenken'sand Sjamaar's partial desingularisation of singular symplecticquotients and a decomposition theorem, proved in Section 2 ofthis paper, exhibiting the intersection cohomology of a symplecticblowup of the singular quotient X along a maximal depthstratum as a direct sum of terms including the intersectioncohomology of X. 相似文献
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In 1903 Minkowski showed that, given pairwise different unitvectors µ1, ..., µm in Euclidean n-space Rn whichspan Rn, and positive reals µ1, ..., µm such thatmi=1µiµi = 0, there exists a polytope P in Rn, uniqueup to translation, with outer unit facet normals µ1, ...,µm and corresponding facet volumes µ1, ..., µm.This paper deals with the computational complexity of the underlyingreconstruction problem, to determine a presentation of P asthe intersection of its facet halfspaces. After a natural reformulationthat reflects the fact that the binary Turing-machine modelof computation is employed, it is shown that this reconstructionproblem can be solved in polynomial time when the dimensionis fixed but is #P-hard when the dimension is part of the input. The problem of Minkowski reconstruction has variousapplications in image processing, and the underlying data structureis relevant for other algorithmic questions in computationalconvexity. 相似文献
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Let T be a bounded linear operator in a complex Banach space.Our main result gives various characterizations of the condition:T is power-bounded and an estimate ||(I – T)Tn || cn–1/2 holds for all positive integers n. In particular, this conditionholds if and only if T = β S + (1 – β)I, forsome β (0, 1) and some power-bounded operator S; or ifand only if T is power-bounded and the discrete semigroup (Tn)is dominated by the continuous semigroup (e– t(I –T))t 0 in a natural sense. As a consequence of our main results,for 1/2 < 1 we characterize the condition that T is power-boundedand ||(I – T)Tn || c n– for all n, in terms ofestimates on the semigroup e–t(I – T). 相似文献
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This paper gives a complete characterization of those sequencesof subword complexity (k – 1)n + 1that are natural codings of orbits of k-interval exchange transformations,thereby answering an old question of Rauzy. 相似文献
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Let C be a genus 2 algebraic curve defined by an equation ofthe form y2 = x(x2 1)(x a)(x 1/a). Asis well known, the five accessory parameters for such an equationcan all be expressed in terms of a and the accessory parameter b corresponding to a. The main result of the paper is thatif a' = 1 a2, which in general yields a non-isomorphiccurve C', then b'a'(a'2 1) = ba(a2 1). This is proven by it being shown how the uniformizing functionfrom the unit disk to C' can be explicitly described in termsof the uniformizing function for C. 相似文献
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We introduce the concept of geometrical spinefor 3-manifolds with natural metrics, in particular, for lensmanifolds. We show that any spine of Lp,q that is close enoughto its geometrical spine contains at least E(p,q) – 3vertices, which is exactly the conjectured value for the complexityc(Lp,q). As a byproduct, we find the minimal rotation distance(in the Sleator–Tarjan–Thurston sense) between atriangulation of a regular p-gon and its image under rotation. 相似文献
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Satisfactory error estimates are obtained from iterative refinementof the solution using Ml, an approximation to the inverseof A and involving ||IM1A||. 相似文献
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Let T : X X be a continuous surjection of a topologicalspace, and let f : X be upper semi-continuous. Wewish to identify those T-invariant measures µ which maximize f dµ. We call such measures f-maximizing, and denotethe maximum by ß(f). The study of such measures andtheir properties has recently been dubbed ergodic optimization.A first step to understanding the structure of a function'smaximizing measures is to establish the following subordinationprinciple defined by T. Bousch: if µ and are T-invariantmeasures such that supp supp µ and µ is f-maximizing,then is also f-maximizing. Previous authors have approachedthis result by constructing a continuous function g : X such that f ß(f) g T g. We providea sufficient condition for the subordination principle whichhas advantages when the space X is noncompact. 相似文献
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The purpose of this paper is to show how the methods of motivicintegration of Kontsevich, DenefLoeser (Invent. Math.135 (1999) 201232 and Compositio Math. 131 (2002) 267290)and Looijenga (Astérisque 276 (2002) 267297) canbe adapted to prove the McKayRuan correspondence, a generalizationof the McKayReid correspondence to orbifolds that arenot necessarily global quotients. 2000 Mathematics Subject Classification14A20, 14E15, 14F43. 相似文献
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The purpose of this note is initially to present an elementarybut surprising connectedness principle pertaining to the intersectionof a fixed subvariety X of some ambient space Z with anothersubvariety Y which is mobile (in the sense ofbeing movable, rather than actually moving). It is via thismobility that monodromy enters the picture, permitting the crucialpassage from relative or total-space irreducibilityto absolute or fibrewise connectedness (and sometimesirreducibility). A general form of this principle is given inTheorem 2 below. 1991 Mathematics Subject Classification 14C99,15N05. 相似文献
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Given a finite function germ f:(X, 0) (, 0) on a reduced spacecurve singularity (X, 0), we show that µ(f) = µ(X,0) + deg(f) – 1. Here, µ(f) and µ(X, 0) denotethe Milnor numbers of the function and the curve, respectively,and deg(f) is the degree of f. We use this formula to obtainseveral consequences related to the topological triviality andWhitney equisingularity of families of curves and families offunctions on curves. 相似文献
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This paper investigates how to relate the syzygy periodicityof a self-injective algebra A to its AuslanderReitenperiodicity. Moreover, a characterization is provided of theAuslanderReiten bounded AA-bimodules that areperiodic. 2000 Mathematics Subject Classification 16G70, 16E40(primary), 16G20 (secondary). 相似文献
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Nearly four hundred years ago, the cubic close-packing of equalspheres in R3 was discovered by Kepler [21], in which each spheretouches 12 others. In 1694, Gregory and Newton discussed thefollowing thirteen spheres problem. Can a rigid material spherebe brought into contact with 13 other such spheres of the samesize? Gregory believed yes, while Newton thoughtno. 1991 Mathematics Subject Classication 11H31,52C17. 相似文献
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This work, investigates the asymptotics for Eulers q-exponentialEq(z), Ramanujans function Aq(z), Jacksons q-Besselfunction Jv(2) (z; q), the Stieltjes–Wigert orthogonalpolynomials Sn(x; q) and q-Laguerre polynomials Ln() (x; q)as q approaches 1. 相似文献
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The paper considers n-dimensional hypersurfaces with constantscalar curvature of a unit sphere Sn1(1). The hypersurfaceSk(c1)xSnk(c2) in a unit sphere Sn+1(1) is characterized,and it is shown that there exist many compact hypersurfaceswith constant scalar curvature in a unit sphere Sn+1(1) whichare not congruent to each other in it. In particular, it isproved that if M is an n-dimensional (n > 3) complete locallyconformally flat hypersurface with constant scalar curvaturen(n1)r in a unit sphere Sn+1(1), then r > 12/n,and (1) when r (n2)/(n1), if
then M is isometric to S1xSn1(c),where S is the squared norm of the second fundamental form ofM; (2) there are no complete hypersurfaces in Sn+1(1) with constantscalar curvature n(n1)r and with two distinct principalcurvatures, one of which is simple, such that r = (n2)/(n1)and
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19.
We study interpolating sequences in the unit ball for A–pwith p > 0, the Banach space of holomorphic functions f with(1 – |z|2)p |f(z)| bounded. The finite unions of A–p-interpolatingsequences are characterized by a Carleson type condition. 相似文献
20.
Let µ be a positive bounded Borel measure on a subsetI of the real line and = {1, ..., n} a sequence of arbitrary complexpoles outside I. Suppose {1, ..., n} is the sequence of rationalfunctions with poles in orthonormal on I with respect to µ. First, we are concernedwith reducing the number of different coefficients in the three-termrecurrence relation satisfied by these orthonormal rationalfunctions. Next, we consider the case in which I = [–1, 1] and µ satisfies the Erdos–Turán conditionµ' > 0 a.e. on I (where µ' is the Radon–Nikodymderivative of the measure µ with respect to the Lebesguemeasure) to discuss the convergence of n+1(x)/n(x) as n tendsto infinity and to derive asymptotic formulas for the recurrencecoefficients in the three-term recurrence relation. Finally,we give a strong convergence result for n(x) under the morerestrictive condition that µ satisfies the Szeg condition(1 – x2)–1/2 log µ'(x) L1([– 1, 1]). 相似文献