共查询到20条相似文献,搜索用时 31 毫秒
1.
Chan-nan Chang 《Journal of Number Theory》1973,5(6):456-476
Let L be a lattice over the integers of a quaternion algebra with center K which is a -adic field. Then the unitary group U(L) equals its own commutator subgroup and is generated by the unitary transvections and quasitransvections contained in it. Let g be a tableau, U(g), U+(g), , T(g) be the corresponding congruence subgroups of order g. Then , and (the subgroup generated by the unitary transvections and quasitransvections with order ≤ g). Let G be a subgroup of U(L) with o(G) = g, then G is normal in U(L) if and only if U(g) ? G ? T(g). 相似文献
2.
William E Strawderman 《Journal of multivariate analysis》1974,4(3):255-264
Families of minimax estimators are found for the location parameters of a p-variate distribution of the form , where G(·) is a known c.d.f. on (0, ∞), p ≥ 3 and the loss is sum of squared errors. The estimators are of the form where 0 ≤ a ≤ 2, r(X′X) is nondecreasing, and is nonincreasing. Generalized Bayes minimax estimators are found for certain G(·)'s. 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.
Nicolae Dinculeanu 《Journal of Functional Analysis》1973,12(3):229-235
Let (X, ∑, μ) be a measure space and S be a semigroup of measure-preserving transformations T:X → X. In case μ(X) < ∞, Aribaud [1] proved the existence of a positive contractive projection P of L1(μ) such that for every belongs to the closure of the convex hull of the set {}. In this paper we extend this result in three directions: we consider infinite measure spaces, vector-valued functions, and Lp spaces with 1 ? p < ∞, and prove that P is in fact the conditional expectation with respect to the σ-algebra Λ of sets of ∑ which are invariant with respect to all T?S. 相似文献
5.
Joel M Cohen 《Journal of Functional Analysis》1982,48(3):301-309
Let G be a group and g1,…, gt a set of generators. There are approximately (2t ? 1)n reduced words in g1,…, gt, of length ?n. Let be the number of those which represent 1G. We show that exists. Clearly 1 ? γ ? 2t ? 1. is the cogrowth. 0 ? η ? 1. In fact . The entropic dimension of G is shown to be 1 ? η. It is then proved that d(G) = 1 if and only if G is free on g1,…, gt and d(G) = 0 if and only if G is amenable. 相似文献
6.
Let , let , where g2 and g3 are coefficients of the elliptic curve: Y2 = 4X3 ? g2X ? g3 over a finite field and Δ = g23 ? 27g32 and let . Then the p-adic cohomology theory will be applied to compute explicitly the zeta matrices of the elliptic curves, induced by the pth power map on the free -module . Main results are; Theorem 1.1: X2dY and YdX are basis elements for ; Theorem 1.2: YdX, X2dY, Y?1dX, Y?2dX and XY?2dX are basis elements for , where is a lifting of X, and all the necessary recursive formulas for this explicit computation are given. 相似文献
7.
Ivan Singer 《Journal of Mathematical Analysis and Applications》1980,76(2):339-368
We show that, if (F →uX) is a linear system, a convex target set and a convex functional, then, under suitable assumptions, the computation of inf ) can be reduced to the computation of the infimum of h on certain strips or hyperplanes in F, determined by elements of , or of the infima on F of Lagrangians, involving elements of . Also, we prove similar results for a convex system (F →uX) and the convex cone Ω of all non-positive elements in X. 相似文献
8.
Stephen D. Fisher 《Journal of Functional Analysis》1973,12(3):236-245
Let T be the unit circle in the complex plane and let A be a vector space of bounded Lebesgue measurable functions on T. A is said to be invariant under the restricted backward shift if, whenever ? is in A and the 0-th Fourier coefficient of ? vanishes, then is also in A. The theorems of this paper provide a characterization of the uniformly closed subalgebras of C(T) which contain the constants and which are invariant under the restricted backward shift and, a similar characterization of the weak-1 closed subalgebras of L∞(T, dθ) which contain the constants and which are invariant under the restricted backward shift. 相似文献
9.
Harry Dym 《Journal of Functional Analysis》1978,28(1):33-57
Let PT denote the orthogonal projection of L2(R1, dΔ) onto the space of entire functions of exponential type ? T which are square summable on the line with respect to the measure , and let G denote the operator of multiplication by a suitably restricted complex valued function g. It is shown that if is summable, if is locally summable, and if belongs to the span in L∞ of e?iyTH∞:T ? 0, in which h is chosen to be an outer function and h#(γ) agrees with the complex conjugate of h(γ) on the line, then exists and is independent of h for every positive integer n. This extends the range of validity of a formula due to Mark Kac who evaluated this limit in the special case h = 1 using a different formalism. It also extends earlier results of the author which were established under more stringent conditions on h. The conclusions are based in part upon a preliminary study of a more general class of projections. 相似文献
10.
11.
Harry Dym 《Journal of Functional Analysis》1979,31(1):69-100
In this paper we study trace formulas for a class of operators of the form ΠT-GΠT in which G designates multiplication by a suitable restricted d × d matrix valued function G(γ) of γ?R1and ΠT stands for the diagonal d × d matrix (δijPT) of orthogonal projections PT of L2(R1, dδ) onto the space IT(dδ) of entire functions of exponential type ?T which are square summable on the line relative to the measure . It is shown that, for a reasonably large class of h, exists and is independent of the choice of h within the permitted class. These results are then used to study the asymptotic behavior, as T ↑ ∞, of the determinant of I ? ΠTGΠT. 相似文献
12.
C.R Putnam 《Journal of Functional Analysis》1974,17(3):263-273
Let T be a subnormal, nonnormal operator on a Hilbert space and suppose that the point spectrum of is empty. Then there exist vectors x ≠ 0 for which exists and is weakly continuous for all z. It is shown that under certain conditions, the Cauchy integral of this vector function taken around an appropriate contour, not necessarily lying in the resolvent set of , leads to a proper (nontrivial) invariant subspace of . 相似文献
13.
Given a polynomial , we calculate a subspace Gp of the linear space 〈X〉 generated by the indeterminates which is minimal with respect to the property (the algebra generated by Gp, and prove its uniqueness. Furthermore, we use this result to characterize the pairs (P,Q) of polynomials P(X1,…,Xn) and Q(X1,…,Xn) for which there exists an isomorphism T:〈X〉 →〈X〉 that “separates P from Q,” i.e., such that for some k(1<k<n) we can write P and Q as and respectively, where . 相似文献
14.
Larry W. Cusick 《Topology and its Applications》1985,21(1):9-18
We show that if X is a finite CW-complex admitting a fixed point free involution then there is a singly graded spectral sequence with and . As an application we prove that for any n > 0 there is a natural number k(n) such that if n > k(n) and X is a homotopy , then X will not admit a fixed point free involution. 相似文献
15.
16.
A.Larry Wright 《Journal of multivariate analysis》1982,12(2):178-185
Two related almost sure limit theorems are obtained in connection with a stochastic process {ξ(t), ?∞ < t < ∞} with independent increments. The first result deals with the existence of a simultaneous stabilizing function H(t) such that for almost all sample functions of the process. The second result deals with a wide-sense stationary process whose random spectral distributions is ξ. It addresses the question: Under what conditions does converge as T → ∞ for all τ for almost all sample functions? 相似文献
17.
William Layton 《Journal of Mathematical Analysis and Applications》1980,77(1):198-204
Existence and uniqueness of 2π-periodic solutions of , where x(t) is in n and e(t, u, v) is a given vector function, 2π-periodic in t, are shown under conditions on the spectrum of the Hessian of G. The equation is studied using a fixed point theorem in the space L2(0, 2π). One feature of this approach is that no relationship between the delay and the period is necessary. 相似文献
18.
Loren D. Pitt 《Journal of multivariate analysis》1978,8(1):45-54
For Gaussian vector fields {X(t) ∈ Rn:t ∈ Rd} we describe the covariance functions of all scaling limits Y(t) = limα↓0 B?1(α) X(αt) which can occur when B(α) is a d × d matrix function with B(α) → 0. These matrix covariance functions are found to be homogeneous in the sense that for some matrix L and each α > 0, . Processes with stationary increments satisfying (1) are further analysed and are found to be natural generalizations of Lévy's multiparameter Brownian motion. 相似文献
19.
J.R. Tort 《Discrete Mathematics》1983,44(2):181-185
Let X be a set of n elements. Let 3(X) be the set of all triples of X. We define a clique as a set of triples which intersect pairwise in two elements. In this paper we prove that if n?6, the minimum cardinality of a partition of 3(X) into cliques is . 相似文献
20.
Thomas G. Kurtz 《Stochastic Processes and their Applications》1978,6(3):223-240
A variety of continuous parameter Markov chains arising in applied probability (e.g. epidemic and chemical reaction models) can be obtained as solutions of equations of the form where , the Y1 are independent Poisson processes, and N is a parameter with a natural interpretation (e.g. total population size or volume of a reacting solution).The corresponding deterministic model, satisfies Under very general conditions limN→∞XN(t)=X(t) a.s. The process XN(t) is compared to the diffusion processes given by and Under conditions satisfied by most of the applied probability models, it is shown that XN,ZN and V can be constructed on the same sample space in such a way that and 相似文献