首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到10条相似文献,搜索用时 234 毫秒
1.
Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball   总被引:1,自引:0,他引:1  
Weighted Triebel–Lizorkin and Besov spaces on the unitball Bd in d with weights wµ(x)=(1–|x|2)µ–1/2,µ0, are introduced and explored. A decomposition schemeis developed in terms of almost exponentially localized polynomialelements (needlets) {}, {} and it is shown that the membershipof a distribution to the weighted Triebel–Lizorkin orBesov spaces can be determined by the size of the needlet coefficients{f, } in appropriate sequence spaces.  相似文献   

2.
For a scattering system {A, A0} consisting of self-adjoint extensionsA and A0 of a symmetric operator A with finite deficiency indices,the scattering matrix {S()} and a spectral shift function arecalculated in terms of the Weyl function associated with a boundarytriplet for A*, and a simple proof of the Krein–Birmanformula is given. The results are applied to singular Sturm–Liouvilleoperators with scalar and matrix potentials, to Dirac operatorsand to Schrödinger operators with point interactions.  相似文献   

3.
Let G be a complex connected reductive group which is definedover , let be its Lie algebra, and let be the variety of maximaltori of G. For (), let be the variety of tori in whose Liealgebra is orthogonal to with respect to the Killing form.We show, using the Fourier–Sato transform of conical sheaveson real vector bundles, that the ‘weighted Euler characteristic’of () is zero unless is nilpotent, in which case it equals(–1)(dim )/2. Here ‘weighted Euler characteristic’means the sum of the Euler characteristics of the connectedcomponents, each weighted by a sign ± 1 which dependson the real structure of the tori in the relevant component.This is a real analogue of a result over finite fields whichis connected with the Steinberg representation of a reductivegroup.  相似文献   

4.
We prove a nearly optimal bound on the number of stable homotopytypes occurring in a k-parameter semi-algebraic family of setsin R, each defined in terms of m quadratic inequalities. Ourbound is exponential in k and m, but polynomial in . More precisely,we prove the following. Let R be a real closed field and let = {P1, ... , Pm} R[Y1, ... ,Y,X1, ... ,Xk], with degY(Pi) 2, degX(Pi) d, 1 i m. Let S R+k be a semi-algebraic set,defined by a Boolean formula without negations, with atoms ofthe form P 0, P 0, P . Let : R+k Rk be the projection onthe last k coordinates. Then the number of stable homotopy typesamongst the fibers Sx = –1(x) S is bounded by (2mkd)O(mk).  相似文献   

5.
Consider the group scheme where R is an arbitrary commutative ring with 1 0 and a unitx R* acts on R by multiplication. We will study the finiteness properties of subgroups of G(OS)where OS is an S-arithmetic subring of a global function field.The subgroups we are interested in are of the form where Q is a subgroup of OS*. The finiteness propertiesof these metabelian groups can be expressed in terms of the-invariant due to R. Bieri and R. Strebel. Theorem A. Let S be a finite set of places of a global functionfield (regarded as normalized discrete valuations) and OS thecorresponding S-arithmetic ring. Let Q be a subgroup of OS*.Then Q is finitely generated and for all integers n 1 the followingare equivalent:
(1) OS Q is of type FPn;
(2) OS is n-tameas a ZQ-module;
(3) each p S restricts to a non-trivial homomorphism and the set is n-tame.
If these conditions hold for at least one n 1 then the identity holds.} Theorem B. Let r denote the rank of Q. Then the followinghold:
(1) the group OS Q is not of type FPr+1};
(2) if Qhas maximum rank r = |S| –1 then the group OS Q is oftype FPr.
In particular, is of type FP|S| –1 but not of type FP|S|. 1991 Mathematics SubjectClassification: 20E08, 20F16, 20G30, 52A20.  相似文献   

6.
We calculate the triple correlations for the truncated divisorsum R(n). The R(n) behave over certain averages just as theprime counting von Mangoldt function (n) does or is conjecturedto do. We also calculate the mixed (with a factor of (n)) correlations.The results for the moments up to the third degree, and thereforethe implications for the distribution of primes in short intervals,are the same as those we obtained (in the first paper with thistitle) by using the simpler approximation R(n). However, whenR(n) is used, the error in the singular series approximationis often much smaller than what R(n) allows. Assuming the GeneralizedRiemann Hypothesis (GRH) for Dirichlet L-functions, we obtainan ±-result for the variation of the error term in theprime number theorem. Formerly, our knowledge under GRH wasrestricted to -results for the absolute value of this variation.An important ingredient in the last part of this work is a recentresult due to Montgomery and Soundararajan which makes it possiblefor us to dispense with a large error term in the evaluationof a certain singular series average. We believe that our resultson the sums R(n) and R(n) can be employed in diverse problemsconcerning primes.  相似文献   

7.
Skeletons and Central Sets   总被引:1,自引:0,他引:1  
Let be an open proper subset of Rn. Its skeleton is the setof points with more than one nearest neighbour in the complementof its central set is the set of centres in maximal open ballsincluded in . Intuitively, if we think of as a land mass inwhich height is proportional to distance from the sea, its skeletonand central set can be thought of as corresponding to ridgesin the mountains of . In this note I discuss the metric andtopological properties of such sets. I show that any skeletonin Rn is F, and has dimension at most n – 1, by any ofthe usual measures of dimension; that if is bounded and connected,its skeleton and central set are connected; and that separatesRn iff its skeleton does iff its central set does. Any centralset in Rn is a G set of topological dimension at most n –1. In the plane, I show that both skeletons and central setsare locally path-connected, and indeed include many paths offinite length. For any , its central set includes its skeleton;I give examples to show that the central set can be significantlylarger than the skeleton. 1991 Mathematics Subject Classification:54F99.  相似文献   

8.
A function f: Rn R is a connectivity function if the graphof its restriction f|C to any connected C Rn is connected inRn x R. The main goal of this paper is to prove that every functionf: Rn R is a sum of n + 1 connectivity functions (Corollary2.2). We will also show that if n > 1, then every functiong: Rn R which is a sum of n connectivity functions is continuouson some perfect set (see Theorem 2.5) which implies that thenumber n + 1 in our theorem is best possible (Corollary 2.6). Toprove the above results, we establish and then apply the followingtheorems which are of interest on their own. For every dense G-subset G of Rn there are homeomorphisms h1,..., hn of Rn such that Rn = G h1(G) ... hn(G) (Proposition2.4). For every n > 1 and any connectivity function f: Rn R, ifx Rn and > 0 then there exists an open set U Rn such thatx U Bn(x, ), f|bd(U) is continuous, and |(x) – f(y)|< for every y bd(U) (Proposition 2.7). 1991 MathematicsSubject Classification: 26B40, 54C30, 54F45.  相似文献   

9.
Algebras and Modules in Monoidal Model Categories   总被引:5,自引:0,他引:5  
In recent years the theory of structured ring spectra (formerlyknown as A- and E-ring spectra) has been simplified by the discoveryof categories of spectra with strictly associative and commutativesmash products. Now a ring spectrum can simply be defined asa monoid with respect to the smash product in one of these newcategories of spectra. In this paper we provide a general methodfor constructing model category structures for categories ofring, algebra, and module spectra. This provides the necessaryinput for obtaining model categories of symmetric ring spectra,functors with smash product, Gamma-rings, and diagram ring spectra.Algebraic examples to which our methods apply include the stablemodule category over the group algebra of a finite group andunbounded chain complexes over a differential graded algebra.1991 Mathematics Subject Classification: primary 55U35; secondary18D10.  相似文献   

10.
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号