共查询到20条相似文献,搜索用时 31 毫秒
1.
Karl J Witsch 《Journal of Mathematical Analysis and Applications》1976,54(3):820-839
Denote by L a second order strongly elliptic operator in the Euclidian p-space p, and by P some real polynomial in one variable. First the wholespace-problem for the equation P(L)u = f is considered and asymptotic conditions are derived which yield an existence and uniqueness theorem. Then for the Dirichlet problem in some exterior domain G ? p a “Fredholm alternative theorem” is proved. 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.
Laurence R Matthews 《Journal of Combinatorial Theory, Series B》1979,27(3):260-273
A matroidal family is defined to be a collection of graphs such that, for any given graph G, the subgraphs of G isomorphic to a graph in satisfy the matroid circuit-axioms. Here matroidal families closed under homeomorphism are considered. A theorem of Simöes-Pereira shows that when only finite connected graphs are allowed as members of , two matroids arise: the cycle matroid and bicircular matroid. Here this theorem is generalized in two directions: the graphs are allowed to be infinite, and they are allowed to be disconnected. In the first case four structures result and in the second case two infinite families of matroids are obtained. The main theorem concerns the structures resulting when both restrictions are relaxed simultaneously. 相似文献
4.
George Benke 《Journal of Functional Analysis》1980,35(3):295-303
In this paper we generalize the classical Bernstein theorem concerning the absolute convergence of the Fourier series of Lipschitz functions. More precisely, we consider a group G which is finite dimensional, compact, and separable and has an infinite, closed, totally disconnected, normal subgroup D, such that is a Lie group. Using this structure, we define in a natural way the notion of Lipschitz condition, and then prove that a function which satisfies a Lipschitz condition of order greater than belongs to the Fourier algebra of G. 相似文献
5.
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
6.
S.Bhaskara Rao 《Discrete Mathematics》1977,17(3):225-233
Let G be a self-complementary graph (s.c.) and π its degree sequence. Then G has a 2-factor if and only if π - 2 is graphic. This is achieved by obtaining a structure theorem regarding s.c. graphs without a 2-factor. Another interesting corollary of the structure theorem is that if G is a s.c. graph of order p?8 with minimum degree at least , then G has a 2-factor and the result is the best possible. 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.
Rüdiger Schmidt 《Discrete Mathematics》1979,27(1):93-97
A matroidal family is a set ≠ ? of connected finite graphs such that for every finite graph G the edge-sets of those subgraphs of G which are isomorphic to some element of are the circuits of a matroid on the edge-set of G. Simões-Pereira [5] shows the existence of four matroidal families and Andreae [1] shows the existence of a countably infinite series of matroidal families. In this paper we show that there exist uncountably many matroidal families. This is done by using an extension of Andreae's theorem, a construction theorem, and certain properties of regular graphs. Moreover we observe that all matroidal families so far known can be obtained in a unified way. 相似文献
9.
Ulrich Höhle 《Fuzzy Sets and Systems》1984,13(1):39-63
Considering complete Boolean algebras as sets of truth values a new concept of compactness—so-called probabilistic compactness — is introduced to -fuzzy topological spaces. The aim of this paper is to show that the most important theorems of the theory of ordinary compact spaces remain true; e.g. probabilistic compactness is preserved under projective limits, every probabilistic compact space has an unique -fuzzy uniformity being compatible with the underlying -fuzzy topology, etc. Finally using the selection theorem due to Kuratowski and Ryll-Nardzewski a non-trivial example of a probabilistic compact space is given. 相似文献
10.
D.R Woodall 《Journal of Combinatorial Theory, Series B》1978,25(2):184-186
A theorem is proved that is (in a sense) the best possible improvement on the following theme: If G is an undirected graph on n vertices in which for every non-empty subset S of the vertices of G, then G is Hamiltonian. 相似文献
11.
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
12.
Let G be any 3-connected graph containing n vertices and r the radius of G. Then the inequality is proved. A similar theorem concerning any (2m ?1)-connected graph G can be proved too. 相似文献
13.
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
14.
David L Ragozin 《Journal of Functional Analysis》1974,17(4):355-376
This paper analyzes the convolution algebra of zonal measures on a Lie group G, with compact subgroup K, primarily for the case when is commutative and is isotropy irreducible. A basic result for such (G, K) is that the convolution of dim continuous (on ) zonal measures is absolutely continuous. Using this, the spectrum (maximal ideal space) of is determined and shown to be in 1-1 correspondence with the bounded Borel spherical functions. Also, certain asymptotic results for the continuous spherical functions are derived. For the special case when G is compact, all the idempotents in are determined. 相似文献
15.
16.
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
17.
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
18.
Carsten Thomassen 《Journal of Combinatorial Theory, Series B》1982,33(2):137-160
Some basic results on duality of infinite graphs are established and it is proven that a block has a dual graph if and only if it is planar and any two vertices are separated by a finite edge cut. Also, the graphs having predual graphs are characterized completely and it is shown that if is a dual and predual graph of G, then G and can be represented as geometric dual graphs. The uniqueness of dual graphs is investigated, in particular, Whitney's 2-isomorphism theorem is extended to infinite graphs. Finally, infinite minimal cuts in dual graphs are studied and the characterization (in terms of planarity and separation properties) of the graphs having dual graphs satisfying conditions on the infinite cuts, as well, is included. 相似文献
19.
Michel Las Vergnas 《Discrete Mathematics》1978,23(3):241-255
We prove the following theorem: Let G be a graph with vertex-set V and ?, g be two integer-valued functions defined on V such that for all x ∈ V. Then G contains a factor F such that for all x ∈ V if and only if for every subset X of V, is at least equal to the number of connected components C of G[V ? X] such that either C = {x} and g(x) = 1, or |C| is odd ?3 and for all x ∈ C. Applications are given to certain combinatorial geometries associated with factors of graphs. 相似文献
20.
In this paper we solve a conjecture of P. Erdös by showing that if a graph Gn has n vertices and at least edges, then G contains a cycle C2l of length 2l for every integer . Apart from the value of the constant this result is best possible. It is obtained from a more general theorem which also yields corresponding results in the case where Gn has only cn(log n)α edges (α ≥ 1). 相似文献