共查询到20条相似文献,搜索用时 406 毫秒
1.
Hugo Beirão da Veiga 《Journal of Functional Analysis》1979,34(1):72-78
We study Fréchet differentiability at the origin, in the Hilbert space , for the Green's operator P and we apply these results to the calculus of bifurcation points. 相似文献
2.
Theodore Laetsch 《Journal of Mathematical Analysis and Applications》1984,102(2):328-347
Positive solutions of the nonlinear eigenvalue problem Au = σu for a forced, convex, isotone, compact operator on a partially ordered locally convex topological vector space E are considered. Denote by the infimum of the set of σ for which the equation has a solution u in the positive cone K of E. is characterized as the saddle value of a functional JA determined by A and defined on the Cartesian product of K and its dual . 相似文献
3.
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
4.
Let C be a convex set in Rn. For each y?C, the cone of C at y, denoted by cone(y, C), is the cone {α(x ? y): α ? 0 and x?C}. If K is a cone in Rn, we shall denote by its dual cone and by F(K) the lattice of faces of K. Then the duality operator of K is the mapping given by . Properties of the duality operator dK of a closed, pointed, full cone K have been studied before. In this paper, we study dK for a general cone K, especially in relation to dcone(y, K), where y?K. Our main result says that, for any closed cone K in Rn, the duality operator dK is injective (surjective) if and only if the duality operator dcone(y, K) is injective (surjective) for each vector y?K ~ [K ∩ (? K)]. In the last part of the paper, we obtain some partial results on the problem of constructing a compact convex set C, which contains the zero vector, such that cone (0, C) is equal to a given cone. 相似文献
5.
Christian Gros 《European Journal of Operational Research》1978,2(5):368-376
For a vector-valued function f, Sup f and Inf f are defined from the Yu's domination theory and the Pareto's efficiency. A notion of conjugate is proposed for convex vector-valued function, this construction gives once more the usual conjugate function: when the function f is scalar. Then, this concept is used to write the Fenchel's problem in convex multiple objective optimization and to prove the associated duality theorem. 相似文献
6.
Let be the n-dimensional ice cream cone, and let Γ(Kn) be the cone of all matrices in nn mapping Kn into itself. We determine the structure of Γ(Kn), and in particular characterize the extreme matrices in Γ(Kn). 相似文献
7.
The spaces in the title are associated to a fixed representing measure m for a fixed character on a uniform algebra. It is proved that the set of representing measures for that character which are absolutely continuous with respect to m is weakly relatively compact if and only if each m-negligible closed set in the maximal ideal space of L∞ is contained in an m-negligible peak set for H∞. J. Chaumat's characterization of weakly relatively compact subsets in therefore remains true, and is complete, under the first conditions. In this paper we also give a direct proof. From this we obtain that has the Dunford-Pettis property. 相似文献
8.
Jean-Louis Nicolas 《Journal of Number Theory》1983,17(3):375-388
Let φ be the Euler's function. A question of Rosser and Schoenfeld is answered, showing that there exists infinitely many n such that , where γ is the Euler's constant. More precisely, if Nk is the product of the first k primes, it is proved that, under the Riemann's hypothesis, holds for any k ≥ 2, and, if the Riemann's hypothesis is false this inequality holds for infinitely many k, and is false for infinitely many k. 相似文献
9.
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
10.
Helmut Strasser 《Journal of multivariate analysis》1975,5(2):206-226
Let (X, ) be a measurable space, Θ ? an open interval and PΩ ∥ , Ω ? Θ, a family of probability measures fulfilling certain regularity conditions. Let be the maximum likelihood estimate for the sample size n. Let λ be a prior distribution on Θ and let be the posterior distribution for the sample size n given . denotes a loss function fulfilling certain regularity conditions and Tn denotes the Bayes estimate relative to λ and L for the sample size n. It is proved that for every compact K ? Θ there exists cK ≥ 0 such that This theorem improves results of Bickel and Yahav [3], and Ibragimov and Has'minskii [4], as far as the speed of convergence is concerned. 相似文献
11.
E.B Dynkin 《Journal of Functional Analysis》1982,47(3):381-418
This is the second paper in a series devoted to Green's and Dirichlet spaces. In the first paper, we have investigated Green's space and the Dirichlet space associated with a symmetric Markov transition function pt(x, B). Now we assume that p is a transition function of a fine Markov process X and we prove that: (a) the space can be built from functions which are right continuous along almost all paths; (b) the positive cone + in can be identified with a cone M of measures on the state space; (c) the positive cone + in can be interpreted as the cone of Green's potentials of measures μ?M. To every measurable set B in the state space E there correspond a subspace (B) of and a subspace (B) of . The orthogonal projections of onto and of onto (B) can be expressed in terms of the hitting probabilities of B by the Markov process X. As the main tool, we use additive functionals of X corresponding to measures μ?M. 相似文献
12.
Wolfgang Dahmen 《Journal of Computational and Applied Mathematics》1984,10(3):255-273
Let Δ denote the triangulation of the plane obtained by multi-integer translates of the four lines x=0, y=0, x=y and x=?y. By we mean the space of all piecewise polynomials of degree ?k with respect to the scaled triangulation hΔ having continuous partial derivatives of order . We show that the approximation properties of are completely governed by those of the space spanned by the translates of all so called box splines contained in . Combining this fact with Fourier analysis techniques allows us to determine the optimal controlled approximation rates for the above subspace of box splines where μ is the largest degree of smoothness for which these spaces are dense as h tends to zero. Furthermore, we study the question of local linear dependence of the translates of the box splines for the above criss-cross triangulations. 相似文献
13.
Tom M. Apostol 《Journal of Number Theory》1982,15(1):14-24
An elementary proof is given of the author's transformation formula for the Lambert series relating Gp(e2πiτ) to Gp(e2πiAτ), where p > 1 is an odd integer and is a general modular substitution. The method extends Sczech's argument for treating Dedekind's function , and uses Carlitz's formula expressing generalized Dedekind sums in terms of Eulerian functions. 相似文献
14.
Hui-Hsiung Kuo 《Journal of Functional Analysis》1973,12(3):246-256
This paper studies the differential equation in infinite dimensional space. A Kac's type representation of solution in terms of function space integral is proved. Kac's method is modified to work nicely regardless of the dimensionality. 相似文献
15.
Pierre A. Vuillermot 《Journal of Mathematical Analysis and Applications》1982,89(1):327-349
Necessary and sufficient conditions are proved for a (2)-Young function G (with independent variable t) to be convex (resp. concave) in t2 in terms of inequalities between the second derivative of G and the first derivative of its Legendre transform G? (with independent variable s). It is then proven that a Young function G is convex (resp. concave) in t2 if and only if G? is concave (resp. convex) in s2. These results, along with another set of inequalities for functions G convex (resp. concave) in t2, allow the proof of the uniform convexity and thereby of the reflexivity with respect to Luxemburg's norm of the Orlicz space over an open domain Ω ?N with Lebesgue measure dξ. When applied to and with p?1 + (p′)?1 = 1, the preceding results lead to the shortest proof to date of two Clarkson's inequalities and of the reflexivity of Lp-spaces for 1 < p < +∞. Finally, some of these results are used to solve by direct methods variational problems associated with the existence question of periodic orbits for a class of nonlinear Hill's equations; these variational problems are formulated on suitable Orlicz-Sobolev spaces and thereby allow for nonlinear terms which may grow faster than any power of the variable. 相似文献
16.
It has been found that interesting mathematical relationships arise from a vectorial generalization of Kirchhoff's and Ohm's laws, in which the “resistors” become Hermitian positive semidefinite (PSD) linear operators. In analogy to the parallel connection of resistors Anderson and Duffin studied the parallel sum R : S of two PSD operators on a finite dimensional space, defined by . Duffin and Trapp then studied the hybrid connection. This paper generalizes some of their results to a much broader class of electrical connections. 相似文献
17.
Hui-Hsiung Kuo 《Journal of multivariate analysis》1982,12(3):415-431
Let and be the spaces of generalized Brownian functionals of the white noises ? and ?, respectively. A Fourier transform from into is defined by ??(?) = ∫1: exp[?i ∫?(t) ?(t) dt]: ), where : : denotes the renormalization with respect to ? and μ is the standard Gaussian measure on the space 1 of tempered distributions. It is proved that the Fourier transform carries ?(t)-differentiation into multiplication by i?(t). The integral representation and the action of?? as a generalized Brownian functional are obtained. Some examples of Fourier transform are given. 相似文献
18.
We investigate the question of which polynomials are not representable as the sum of “few” powers of polynomials. In particular for Waring's problem over the ring of polynomials we show that there exist polynomials which are not the sum of fewer than nth powers of polynomials. 相似文献
19.
Guy Giraud 《Discrete Mathematics》1976,16(1):13-38
On determine le nombre maximum de triangles bicolores quand n tend vers l'infini, soit . On prouve aussi que, pour n assez grand, plus d'un triangle sur vingt-neuf est unicolore le methode suivie est susceptible de constituer une approche du probléme posé par une conjecture d'Erdos. Sos et Turan sur le nombre maximum de triangles tricolores. 相似文献
20.
Motivated by models from stochastic population biology and statistical mechanics, we proved new inequalities of the form , where A and B are n × n complex matrices, 1<n<∞, and ? is a real-valued continuous function of the eigenvalues of its matrix argument. For example, if A is essentially nonnegative, B is diagonal real, and ? is the spectral radius, then (1) holds; if in addition A is irreducible and B has at least two different diagonal elements, then the inequality (1) is strict. The proof uses Kingman's theorem on the log-convexity of the spectral radius, Lie's product formula, and perturbation theory. We conclude with conjectures. 相似文献