共查询到20条相似文献,搜索用时 31 毫秒
1.
Alladi Sitaram 《Journal of Functional Analysis》1978,27(2):179-184
Let G be a semisimple noncompact Lie group with finite center and let K be a maximal compact subgroup. Then W. H. Barker has shown that if T is a positive definite distribution on G, then T extends to Harish-Chandra's Schwartz space 1(G). We show that the corresponding property is no longer true for the space of double cosets . If G is of real-rank 1, we construct liner functionals for each p, 0 < p ? 2, such that but Tp does not extend to a continuous functional on . In particular, if p ? 1, Tv does not extend to a continuous functional on . We use this to answer a question (in the negative) raised by Barker whether for a K-bi-invariant distribution T on G to be positive definite it is enough to verify that . The main tool used is a theorem of Trombi-Varadarajan. 相似文献
2.
William H Barker 《Journal of Functional Analysis》1975,20(3):179-207
Let G be a connected semisimple Lie group with finite center and K a maximal compact subgroup. Denote (i) Harish-Chandra's Schwartz spaces by p(G)(0<p?2), (ii) the K-biinvariant elements in p(G) by p(G), (iii) the positive definite (zonal) spherical functions by , and (iv) the spherical transform on p(G) by ? → gj. For T a positive definite distribution on G it is established that (i) T extends uniquely onto l(G), (ii) there exists a unique measure μ of polynomial growth on such that T[ψ]=∫pψdμ for all ψ?I1(G) (iii) all measures μ of polynomial growth on are obtained in this way, and (iv) T may be extended to a particular p(G) space (1 ? p ? 2) if and only if the support of μ lies in a certain easily defined subset of . These results generalize a well-known theorem of Godement, and the proofs rely heavily on the recent harmonic analysis results of Trombi and Varadarajan. 相似文献
3.
Woody Lichtenstein 《Journal of Functional Analysis》1979,34(3):433-455
For a symmetric space of compact type, the highest-weight vectors for representations of G occurring in become heavily concentrated near certain submanifolds of as the highest weight goes to infinity. This fact is applied to obtain estimates for the spectral measures of the operators qλ = PλqPλ, where is an orthogonal projection onto a G-irreducible summand, and q: G/K → is a continuous function acting on by multiplication. 相似文献
4.
A. Guichardet 《Journal of multivariate analysis》1976,6(1):138-158
The following is an expository paper, containing few and sometimes incomplete proofs, on continuous tensor products of Hilbert spaces and of group representations, and on the irreducibility of the latter; the principal results in the last direction are due to Verchik, Gelfand, and Graiev. The theory of continuous tensor products of Hilbert spaces, based on a fundamental theorem of Araki and Woods, is closely related to that of conditionally positive definite functions; it relies on the technique of symmetric Hilbert spaces, which also can be used to give a new proof of the classical Lévy-Khinchin formula (see A. Guichardet, (1973). J. Multiv.3 249–261.). Another basic tool for what follows is the 1-cohomology of unitary representations of locally compact groups; here, the main results are due to P. Delorme; let us mention, for instance, his results for the case of a group G containing a compact subgroup K such that is commutative, using a Lévy-Khinchin's type formula for K-invariant functions due to Gangolli, Faraut, and Harzallah. We add that the results exposed in that paper should have interesting connections with the central limit theorems à la Parthasarathy-Schmidt (see K. Parthasarathy, (1974). J. Multiv. Anal.4 123–149). 相似文献
5.
Nicole Bopp 《Journal of Functional Analysis》1981,44(3):348-358
Let K be a compact subgroup of the isometry group of n. A distribution T is said to be of K-positif type if it is K-invariant and if for every K-invariant ∞ function ? with compact support. We look for an integral representation of these distributions (i.e., an analog of the Bochner-Schwartz theorem). In this paper we obtain such a representation for distributions with growth of exponential type in the following case: K is the maximal compact subgroup of a semi-simple connected Lie group G with finite center, acting by the adjoint action on the tangent space of . The main step is to prove that it suffices to work with distributions of W-positif type (where W is the Weyl group associated with ). This is achieved following ideas of a paper of S. Helgason [Advan. in Math.36 (1980) 297]. The end of the proof follows from the case where K is finite [N. Bopp, in “Analyse harmonique sur les groupes de Lie,” Lecture Notes in Mathematics No. 739, p. 15, Springer-Verlag, Berlin/New York 1979]. 相似文献
6.
Kenny Koffi Siggini 《Comptes Rendus Mathematique》2002,334(11):949-952
Let be the space of positive -regular set-valued measures defined on a σ-algebra with values in the space of all compact non empty convex subsets of a Banach space E. We characterize the compact subsets of endowed with the weakest topology for which all mappings M→M(A), are continuous. The case of real nonnegative measures has been investigated by Topsøe [6], Grothendieck [3] and others. To cite this article: K.K. Siggini, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 949–952. 相似文献
7.
We find necessary and sufficient conditions for a finite K–bi–invariant measure on a compact Gelfand pair (G,K) to have a square–integrable density. For convolution semigroups, this is equivalent to having a continuous density in positive time. When (G,K) is a compact Riemannian symmetric pair, we study the induced transition density for G–invariant Feller processes on the symmetric space X = G/K. These are obtained as projections of K–bi–invariant Lévy processes on G, whose laws form a convolution semigroup. We obtain a Fourier series expansion for the density, in terms of spherical functions, where the spectrum is described by Gangolli’s Lévy–Khintchine formula. The density of returns to any given point on X is given by the trace of the transition semigroup, and for subordinated Brownian motion, we can calculate the short time asymptotics of this quantity using recent work of Bañuelos and Baudoin. In the case of the sphere, there is an interesting connection with the Funk–Hecke theorem. 相似文献
8.
Margit Rösler 《Journal of Functional Analysis》2010,258(8):2779-2800
In this paper, we derive explicit product formulas and positive convolution structures for three continuous classes of Heckman-Opdam hypergeometric functions of type BC. For specific discrete series of multiplicities these hypergeometric functions occur as the spherical functions of non-compact Grassmann manifolds G/K over one of the skew fields F=R,C,H. We write the product formula of these spherical functions in an explicit form which allows analytic continuation with respect to the parameters. In each of the three cases, we obtain a series of hypergroup algebras which include the commutative convolution algebras of K-biinvariant functions on G as special cases. The characters are given by the associated hypergeometric functions. 相似文献
9.
The class [S] of locally compact groups G is considered, for which the algebra L1(G) is symmetric (=Hermitian). It is shown that [S] is stable under semidirect compact extensions, i.e., H ? [S] and K compact implies K ×sH? [S]. For connected solvable Lie groups inductive conditions for symmetry are given. A construction for nonsymmetric Banach algebras is given which shows that there exists exactly one connected and simply solvable Lie group of dimension ?4 which is not in [S]. This example shows that [S]. Z the center of G, in general does not imply G ?[S]. It is shown that nevertheless for discrete groups and a (possibly) stronger form of symmetry this implication holds, implying a new and shorter proof of the fact that [S] contains all discrete nilpotent groups. 相似文献
10.
We consider a real semi-simple Lie group G with finite center and a maximal compact sub-group K of G. Let be a Cartan decomposition of G. For x∈G denote ∥x∥ the norm of the -component of x in the Cartan decomposition of G. Let and 1?p,q?∞. In this Note we give necessary and sufficient conditions on such that for all K-bi-invariant measurable function f on G, if ea∥x∥2f∈Lp(G) and then f=0 almost everywhere. To cite this article: S. Ben Farah, K. Mokni, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
11.
G = 〈V(G), E(G)〉 denotes a directed graph without loops and multiple arrows. (G) denotes the set of all Hamiltonian circuits of G. Put H(n, r) = max{|E(G)|, |V(G)| = n, 1 ≤ |(G)| ≤ r}. Theorem: . Further, H(n, 2),…, H(n, 5) are given. 相似文献
12.
M.Z Nashed 《Journal of Mathematical Analysis and Applications》1976,53(2):359-366
Let K(s, t) be a continuous function on [0, 1] × [0, 1], and let be the linear integral operator induced by the kernel K(s, t) on the space 2[0, 1]. This note is concerned with moment-discretization of the problem of minimizing 6Kx?y6 in the 2-norm, where y is a given continuous function. This is contrasted with the problem of least-squares solutions of the moment-discretized equation: ∝01K(si, t) x(t) dt = y(si), i = 1, 2,h., n. A simple commutativity result between the operations of “moment-discretization” and “least-squares” is established. This suggests a procedure for approximating (where 2 is the generalized inverse of ), without recourse to the normal equation , that may be used in conjunction with simple numerical quadrature formulas plus collocation, or related numerical and regularization methods for least-squares solutions of linear integral equations of the first kind. 相似文献
13.
William T. Stout 《Journal of Number Theory》1973,5(2):116-122
Let K and K′ be number fields with L = K · K′ and F = KφK′. Suppose that and are normal extensions of degree n. Let be a prime ideal in L and suppose that is totally ramified in and in . Let π be a prime element for K = φ K, and let f(x) ∈ F[x] be the minimum polynomial for π over F. Suppose that K · L = (≠)e. Then, , where and m is the largest integer such that (K′)nm/e φ f(K′) ≠ {φ}.If we assume in addition to the above hypotheses that [K : F] = [K′: F] = pn, a prime power, and that divides p and is totally ramified in , then , with t = t( : L/F). 相似文献
14.
Alan L.T Paterson 《Journal of Functional Analysis》1983,53(3):203-223
A theory of harmonic analysis on a metric group (G, d) is developed with the model of U, the unitary group of a C1-algebra , in mind. Essential in this development is the set of contractive, irreducible representations of G, and its concomitant set Pd(G) of positive-definite functions. It is shown that is compact and closed in . The set is determined in a number of cases, in particular when G = U() with abelian. If is an AW1-algebra, it is shown that d is essentially the same as . Unitary groups are characterised in terms of a certain Lie algebra u and several characterisations of G = U() when is abelian are given. 相似文献
15.
P Delorme 《Journal of Functional Analysis》1978,30(1):36-47
Étant donné un groupe localement compact G et un espace mesuré (X, μ) avec μ non atomique, notons G(x) le groupe des applications mesurables de X dans G ne prenant qu'un nombre fini de valeurs. Il existe une méthode pour construire des représentations unitaires de G(x) qui soient invariantes (àéquivalence unitaire près) par toutes les permutations de X conservant μ. Cette construction utilise la théorie des produits tensoriels continus de représentations; en gros, on sait associer une telle représentation à tout triplet (A, b, c) où A est une représentation unitaire de G, b un 1-cocycle pout A et c une application de G dans qui vérifie . Verchik, Gelfand Graiev ont démontré (Funk. An. igo Priloz.8 (1974), 67–69) que est irreductible si b(G) est total dans l'espace de A et si de plus G contient un sous groupe compact K tel que b restreint à K soit nul et ne contient pas la représentation triviale.Dans le présent article, nous démontrons un théorème de structure du commutant de ; pour cela nous utilisons la théorie des formes standards des algèbres de Von Neumann ainsi qu'un théorème de Araki et Woods sur les algèbres booléennes complètes de facteurs de type I. Comme corollaire nous retrouvons le résultat précité de Verchik, Gelfand, Graiev et d'autre part que est irréductible dès que A (non triviale) a la même propriété et que b n'est pas un cobord. 相似文献
16.
For finite graphs F and G, let NF(G) denote the number of occurrences of F in G, i.e., the number of subgraphs of G which are isomorphic to F. If and are families of graphs, it is natural to ask then whether or not the quantities NF(G), F∈, are linearly independent when G is restricted to . For example, if = {K1, K2} (where Kn denotes the complete graph on n vertices) and is the family of all (finite) trees, then of course NK1(T) ? NK2(T) = 1 for all T∈. Slightly less trivially, if = {Sn: n = 1, 2, 3,…} (where Sn denotes the star on n edges) and again is the family of all trees, then Σn=1∞(?1)n+1NSn(T)=1 for all T∈. It is proved that such a linear dependence can never occur if is finite, no F∈ has an isolated point, and contains all trees. This result has important applications in recent work of L. Lovász and one of the authors (Graham and Lovász, to appear). 相似文献
17.
Dana P Williams 《Journal of Functional Analysis》1981,41(1):40-76
We obtain several results characterizing when transformation group C1-algebras have continuous trace. These results can be stated most succinctly when () is second countable, and the stability groups are contained in a fixed abelian subgroup. In this case, has continuous trace if and only if the stability groups vary continuously on Ω and compact subsets of Ω are wandering in an appropriate sense. In general, we must assume that the stability groups vary continuously, and if () is not second countable, that the natural maps of onto G · x are homeomorphisms for each x. Then has continuous trace if and only if compact subsets of Ω are wandering and an additional C1-algebra, constructed from the stability groups and Ω, has continuous trace. 相似文献
18.
William B. Jones Olav Njåstad W.J. Thron 《Journal of Computational and Applied Mathematics》1983,9(2):105-123
Each member G(z) of a family of analytic functions defined by Stieltjes transforms is shown to be represented by a positive T-fraction, the approximants of which form the main diagonal in the two-point Padé table of G(z). The positive T-fraction is shown to converge to G(z) throughout a domain D(a, b) = [z: z?[?b, ?a]], uniformly on compact subsets. In addition, truncation error bounds are given for the approximants of the continued function; these bounds supplement previously known bounds and apply in part of the domain of G(z) not covered by other bounds. The proofs of our results employ properties of orthogonal -polynomials (Laurent polynomials) and -Gaussian quadrature which are of some interest in themselves. A number of examples are considered. 相似文献
19.
Wolfgang Ruess 《Journal of Mathematical Analysis and Applications》1981,84(2):400-417
This is a study of compactness in (a) spaces Kb(X, Y) of compact linear operators, (b) injective tensor products , and (c) spaces Lc(X, Y) of continuous linear operators, and its various relationships with equicontinuity and collective compactness. Among the applications is a result on factoring compact sets of compact operators compactly and uniformly through one and the same reflexive Banach space. 相似文献
20.
Florent Bernon 《Comptes Rendus Mathematique》2002,334(11):945-948
We consider a symplectic group Sp and an reductive and irreductible dual pair (G,G′) in Sp in the sense of R. Howe. Let (resp. ) be the Lie algebra of G (resp. G′). T. Przebinda has defined a map , called the Cauchy Harish-Chandra integral from the space of smooth compactly supported functions of to the space of functions defined on the open set of semisimple regular elements of . We prove that these functions are invariant integrals if G and G′ are linear groups and they behave locally like invariant integrals if G and G′ are unitary groups of same rank. In this last case, we obtain the jump relations up to a multiplicative constant which only depends on the dual pair. To cite this article: F. Bernon, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 945–948. 相似文献