共查询到20条相似文献,搜索用时 31 毫秒
1.
Christopher Meaney 《Journal of Functional Analysis》1982,48(1):43-57
Let G be a compact connected semisimple Lie group with Lie algebra . We show that the conjugacy class of a regular element of G is not a set of synthesis for the Fourier algebra of G. Similarly, the Ad(G)-orbit of a regular element of is not a set of synthesis for the algebra of Fourier transforms on . In proving this latter result we demonstrate a regularity property of Ad-invariant Fourier transforms, analogous to the differentiability of radial Fourier transforms. 相似文献
2.
George Benke 《Journal of Functional Analysis》1978,29(3):319-327
In this paper we study in the context of compact totally disconnected groups the relationship between the smoothness of a function and its membership in the Fourier algebra G. Specifically, we define a notion of smoothness which is natural for totally disconnected groups. This in turn leads to the notions of Lipshitz condition and bounded variation. We then give a condition on α which if satisfied implies Lipα(G) ? (G). On certain groups this condition becomes: (Bernstein's theorem). We then give a similar condition on α which if satisfied implies that Lipα(G) ∈ BV(G) ? (G). On certain groups this condition becomes: α > 0 (Zygmund's theorem). Moreover we show that is best possible by showing that ? (G). 相似文献
3.
Niels Juul Munch 《Journal of Functional Analysis》1983,52(3):413-419
Let G be a finite Abelian group acting by tensor-product automorphisms on a UHF-C1-algebra . Extending a result of A. Kishimoto it is shown that the number of extremal traces on the fixed-point algebra G equals the cardinality of the subgroup K of automorphisms in G which are weakly inner in the trace representation of . 相似文献
4.
Jean-Yves Charbonnel 《Journal of Functional Analysis》1981,41(2):175-203
Let G be a connected solvable Lie group, π a normal factor representation of G and ψ a nonzero trace on the factor generated by G. We denote by (G) the space of C∞ functions on G which are compactly supported. We show that there exists an element u of the enveloping algebra U of the complexification of the Lie algebra of G for which the linear form on (G) is a nonzero semiinvariant distribution on G. The proof uses results about characters for connected solvable Lie groups and results about the space of primitive ideals of the enveloping algebra U. 相似文献
5.
C.D Godsil 《Journal of Combinatorial Theory, Series B》1980,29(1):116-140
Let X be a vertex-transitive graph with complement . We show that if both N, the neighbourhood of a vertex in X, and , the neighbourhood of a vertex in , are disconnected, then either X is isomorphic to K3 × K3 or both N and contain isolated vertices. We characterize the graphs which satisfy this last condition and show in consequence that they admit automorphisms of the form (12)(34). It follows that if X is a GRR for some graph G then at least one of N and is connected. (X is said to be a graphical regular representation, or GRR, for G if its automorphism group is isomorphic to G and acts regularly on its vertices.) Using this result we determine those groups generated by their involutions which do not have a GRR. The largest such group has order 18. As a corollary we conclude that all non-abelian simple groups have GRR's. 相似文献
6.
Niels Vigand Pedersen 《Journal of Functional Analysis》1981,43(3):368-393
For an arbitrary separable locally compact group G we exhibit a canonical Borel subset of the quasi-dual (with the Mackey Borel structure), such that is a standard Borel space in the induced Borel structure, and such that the canonical measure for the left regular representation λGof G is concentrated on . On the basis of this we discuss the (non-unimodular) “Plancherel theorem.” 相似文献
7.
Let G be a finite abelian group. We investigate those graphs admitting G as a sharply 1-transitive automorphism group and all of whose eigenvalues are rational. The study is made via the rational algebra (G) of rational matrices with rational eigenvalues commuting with the regular matrix representation of G. In comparing the spectra obtainable for graphs in (G) for various G's, we relate subschemes of a related association scheme, subalgebras of (G), and the lattice of subgroups of G. One conclusion is that if the order of G is fifth-power-free, any graph with rational eigenvalues admitting G has a cospectral mate admitting the abelian group of the same order with prime-order elementary divisors. 相似文献
8.
J.F. Colombeau 《Journal of Mathematical Analysis and Applications》1983,94(1):96-115
If Ω denotes an open subset of n (n = 1, 2,…), we define an algebra (Ω) which contains the space ′(Ω) of all distributions on Ω and such that is a subalgebra of (Ω). The elements of (Ω) may be considered as “generalized functions” on Ω and they admit partial derivatives at any order that generalize exactly the derivation of distributions. The multiplication in (Ω) gives therefore a natural meaning to any product of distributions, and we explain how these results agree with remarks of Schwartz on difficulties concerning a multiplication of distributions. More generally if q = 1, 2,…, and —a classical Schwartz notation—for any G1,…,Gq∈G(σ), we define naturally an element . These results are applied to some differential equations and extended to the vector valued case, which allows the multiplication of vector valued distributions of physics. 相似文献
9.
U. Cattaneo 《Journal of Functional Analysis》1980,35(2):143-152
The possibility of endowing an Abelian topological group G with the structure of a topological vector space when a subgroup F of G and the quotient group are topological vector groups is investigated. It is shown that, if F is a real Fréchet group and a complete metrizable real vector group, then G is a complete metrizable real vector group. This result is of particular interest if is finite dimensional or if F is one dimensional and a separable Hilbert group. 相似文献
10.
11.
Ethelbert N Chukwu Jan M Gronski 《Journal of Mathematical Analysis and Applications》1977,61(1):97-112
The research deals with complete and approximate controllability of the system , without control restraints to an arbitrary convex target set. First, some characterizations of complete controllability, to the target of (1) and a special case of (1) namely are given. As a consequence complete controllability is equivalent to null-controllability. Next certain equations are formulated. These are in the same spirit as J. P. Dauer's “A Controllability Technique for Nonlinear Systems” (J. Math. Anal. Appl. oo (1972), 442–451) and are utilized in the main contribution of the paper: Under certain convexity assumption, bounded perturbations of systems which are completely controllable to a fixed target G are completely controllable to G. Without the convexity assumption, but with perturbations satisfying a Lipschitz condition, approximate controllability to G of a perturbed system is equivalent to complete controllability to G of the unperturbed equation. 相似文献
12.
A function diagram (f-diagram) D consists of the family of curves {ñ} obtained from n continuous functions . We call the intersection graph of D a function graph (f-graph). It is shown that a graph G is an f-graph if and only if its complement ? is a comparability graph. An f-diagram generalizes the notion of a permulation diagram where the fi are linear functions. It is also shown that G is the intersection graph of the concatenation of ?k permutation diagrams if and only if the partial order dimension of . Computational complexity results are obtained for recognizing such graphs. 相似文献
13.
Stephen M Paneitz 《Journal of Functional Analysis》1981,43(3):313-359
The convex cones in a simple Lie algebra invariant under the adjoint group G of are studied. Using a earlier abstract classification of such cones, we find explicit algebraic presentations of such cones in all the classical hermitian symmetric Lie algebras. (Nontrivial such cones exist only in these cases.) The G-orbits in such cones are listed. The notion of a temporal action of a Lie group with an invariant causal orientation upon a causally oriented manifold is defined. The canonical actions of such classical groups G as above on the S?hilov boundaries of the associated (tube-type) hermitian symmetric spaces are shown to be temporal actions. Corollaries are (1) the existence of nontrivial (Lie) semigroups S in the infinite-sheeted coverings of G, which are invariant under conjugation by and satisfy S ∩ S?1 = {e}, and (2) the global causality (i.e. no “closed time-like curves”) of such covering groups . 相似文献
14.
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
15.
Let Π(G) be the set of paths of a particular class Π from the initial to the terminal root of a two-rooted (possibly directed) graph G. We consider the family of -weights defined by where Πx(G) is the family of subsets of Π(G) which cover x(G), the vertex set or the edge (arc) set of G.A number of the common properties and interrelations of these weights are discussed. Some of the weights have been considered previously, [1, 2], in the context of percolation theory but here only combinatorial arguments are used. 相似文献
16.
Let be the group of orientation-preserving diffeomorphisms of the circle S1. Then is Fréchet Lie group with Lie algebra (δ∞)R the smooth real vector fields on S1. Let δR be the subalgebra of real vector fields with finite Fourier series. It is proved that every infinitesimally unitary projective positive-energy representation of δR integrates to a continuous projective unitary representation of . This result was conjectured by V. Kac. 相似文献
17.
Suppose G is a separable locally compact group and N is a closed normal subgroup. If the dual N? is smooth and the orbit space is smooth for the natural action of G on , the method of G. W. Mackey (Acta Math.99 (1958), 265–311) gives a fairly simple procedure for constructing the dual ?. In this paper we examine an example which shows that the nonseparable case is much more complicated. In the example, N is abelian, is finite and even when the stabilizer is N there are many irreducible representations of G associated with the same orbit. 相似文献
18.
David Lee DeGeorge 《Journal of Functional Analysis》1982,48(1):81-94
Osborne and Warner have given a formula for the multiplicity of an integrable discrete series representation in when G is real rank one semi-simple Lie group and Γ is a discrete subgroup of co-finite volume. We simplify and evaluate this formula to show that for most G (as above) the multiplicity is the formal degree of the representation times the volume of . When it is not we give a simple interpretation of the difference. 相似文献
19.
CAI Mao-cheng 《Discrete Mathematics》1984,49(1):15-20
Given a finite loopless graph G (resp. digraph D), let σ(G), ?(G) and ψ(D) denote the minimal cardinalities of a completely separating system of G, a separating system of G and a separating system of D, respectively. The main results of this paper are: denotes the chromatic number of G. (ii) All the problems of determining σ(G), ?(G) and ψ(D) are NP-complete. 相似文献
20.
We show that for a C1-dynamical system (A, G, α) with G discrete (abelian) the Connes spectrum Γ(α) is equal to if and only if every nonzero closed ideal in G × αA has a nonzero intersection with A. Denote by GJ the closed subgroup of G that leaves fixed the primitive ideal J of A. We show for a general group G that if all isotropy groups GJ are discrete, then GXαA is simple if and only if A is G-simple and . This result is applicable not only when G is discrete but also when G? or G? provided that A is not primitive. Specializing to single automorphisms (i.e., G=) we show that if (the transposed of) α acts freely on a dense set of points in , then Λ(α)=. The converse is only proved when A is of type I. 相似文献