共查询到20条相似文献,搜索用时 31 毫秒
1.
Werner Müller 《Comptes Rendus Mathematique》2004,338(5):347-352
Let Γ be a principal congruence subgroup of and let σ be an irreducible unitary representation of SO(n). Let NcusΓ(λ,σ) be the counting function of the eigenvalues of the Casimir operator acting in the space of cusp forms for Γ which transform under SO(n) according to σ. In this Note we prove that the counting function NcusΓ(λ,σ) satisfies Weyl's law. In particular, this implies that there exist infinitely many cusp forms for the full modular group . To cite this article: W. Müller, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
2.
Alexander Litvak Alain Pajor Mark Rudelson Nicole Tomczak-Jaegermann Roman Vershynin 《Comptes Rendus Mathematique》2004,339(1):33-38
Let be the space equipped with a norm 6·6 whose unit ball has a bounded volume ratio with respect to the Euclidean unit ball. Let Γ be any random N×n matrix with N>n, whose entries are independent random variables satisfying some moment assumptions. We show that with high probability Γ is a good isomorphism from the n-dimensional Euclidean space onto its image in : there exist α,β>0 such that for all , . This solves a conjecture of Schechtman on random embeddings of ?2n into ?1N. To cite this article: A. Litvak et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献
3.
If θ is a norm on Cn, then the mapping from Mn(C) (=Cn × n) into R is called the logarithmic derivative induced by the vector norm θ. In this paper we generalize this concept to a mapping γ from Mn(C) into Mk(R), where k ? n. Denoting by α(B) the spectral abscissa of a square matrix B (the largest of the real parts of the eigenvalues), we show, in particular, that α(A) ?α(γ(A)). As a byproduct we obtain simple sufficient conditions for the stability of a matrix. 相似文献
4.
The authors consider irreducible representations of a nilpotent Lie group and define a Fourier transform for Schwartz class (and other) functions φ on N by forming the kernels Kφ(x, y) of the trace class operations πφ = ∝Nφ(n)πndn, regarding the π as modeled in L2(Rk) for all π in general position. For a special class of groups they show that the models, and parameters λ labeling the representations in general position, can be chosen so the joint behavior of the kernels Kφ(x, y, λ) can be interpreted in a useful way. The variables (x, y, λ) run through a Zariski open set in Rn, n = dim N. The authors show there is a polynomial map u = A(x, y, λ) that is a birational isomorphism A: Rn → Rn with the following properties. The Fourier transforms F1φ = Kφ(x, y, λ) all factor through A to give “rationalized” Fourier transforms Fφ(u) such that Fφ ° A = F1φ. On the rationalized parameter space a function f(u) is of the form Fφ = f ? f is Schwartz class on Rn. If polynomial operators T?P(N) are transferred to operators on Rn such that is transformed isomorphically to P(Rn). 相似文献
5.
A function f(x) defined on = 1 × 2 × … × n where each i is totally ordered satisfying f(x ∨ y) f(x ∧ y) ≥ f(x) f(y), where the lattice operations ∨ and ∧ refer to the usual ordering on , is said to be multivariate totally positive of order 2 (MTP2). A random vector Z = (Z1, Z2,…, Zn) of n-real components is MTP2 if its density is MTP2. Classes of examples include independent random variables, absolute value multinormal whose covariance matrix Σ satisfies ?DΣ?1D with nonnegative off-diagonal elements for some diagonal matrix D, characteristic roots of random Wishart matrices, multivariate logistic, gamma and F distributions, and others. Composition and marginal operations preserve the MTP2 properties. The MTP2 property facilitate the characterization of bounds for confidence sets, the calculation of coverage probabilities, securing estimates of multivariate ranking, in establishing a hierarchy of correlation inequalities, and in studying monotone Markov processes. Extensions on the theory of MTP2 kernels are presented and amplified by a wide variety of applications. 相似文献
6.
R Michel 《Journal of multivariate analysis》1979,9(3):401-409
Let Pη, η = (θ, γ) ∈ Θ × Γ ? × k, be a (k + 1)-dimensional exponential family. Let , n ∈ , be an optimal similar test for the hypothesis {P(θ,γ)n: γ ∈ Γ} (θ ∈ Θ fixed) against alternatives P(θ1,γ1)n, θ1 > θ, γ1 ∈ Γ. It is shown that (?n1)n∈ is third order efficient in the class of all test-sequences that are asymptotically similar of level α + o(n?1) (locally uniformly in the nuisance parameter γ). 相似文献
7.
Let B(H) be the bounded operators on a Hilbert space H. A linear subspace R ? B(H) is said to be an operator system if 1 ?R and R is self-adjoint. Consider the category of operator systems and completely positive linear maps. R ∈ is said to be injective if given A ? B, A, B ∈ , each map A → R extends to B. Then each injective operator system is isomorphic to a conditionally complete C1-algebra. Injective von Neumann algebras R are characterized by any one of the following: (1) a relative interpolation property, (2) a finite “projectivity” property, (3) letting Mm = B(Cm), each map R → N ? Mm has approximate factorizations R → Mn → N, (4) letting K be the orthogonal complement of an operator system N ? Mm, each map has approximate factorizations . Analogous characterizations are found for certain classes of C1-algebras. 相似文献
8.
Using old results on the explicit calculation of determinants, formulae are given for the coefficients of P0(z) and P0(z)fi(z) ? Pi(z), where Pi(z) are polynomials of degree σ ? ρi (i=0,1,…,n), P0(z)fi(z) ? Pi(z) are power series in which the terms with zk, 0?k?σ, vanish (i=1,2,…,n), (ρ0,ρ1,…,ρn) is an (n+1)-tuple of nonnegative integers, σ=ρ0+ρ1+?+ρn, and {fi}ni=1 is the set of hypergeometric functions {1F1(1;ci;z)}ni=1 or {2F0(ai,1;z)}ni=1 under the condition ρ0?ρi ? 1 (i=1,2,…,n). 相似文献
9.
The set Vkn of all n-tuples (x1, x2,…, xn) with xi?, k is considered. The problem treated in this paper is determining σ(n, k), the minimum size of a set W ? Vkn such that for each x in Vkn, there is an element in W that differs from x in at most one coordinate. By using a new constructive method, it is shown that σ(n, p) ? (p ? t + 1)pn?r, where p is a prime and for some integers t and r. The same method also gives σ(7, 3) ? 216. Another construction gives the inequality σ(n, kt) ? σ(n, k)tn?1 which implies that σ(q + 1, qt) = qq?1tq when q is a prime power. By proving another inequality σ(np + 1, p) ? σ(n, p)pn(p?1), σ(10, 3) ? 5 · 36 and σ(16, 5) ? 13 · 512 are obtained. 相似文献
10.
The authors give a new method for calculating the spectrum and multiplicities of the irreducible unitary representations appearing in the quasi-regular representation U: N × L2(ΓβN) → L2(ΓβN) on a compact nilmanifold ΓβN. They proceed by decomposing the trace of U into traces of irreducible representations. The basic calculations in the paper deal with lattice subgroups (Λ = log Γ an additive lattice in the Lie algebra ), essentially using the Poisson summation formula. Let Ad′ be the contragredient adjoint action of N on 1. If ?0 ? 1, the multiplicity of π(?0) in U is zero unless the Ad′(N) orbit of ?0 meets . If ?0 ? Λ⊥, then the multiplicity is a sum over representatives of certain Ad′(Γ)-orbits in, .The constants are given both algebraic and geometric interpretations that lead to simple and effective calculations. Similar formulas hold if Γ is not a lattice subgroup. 相似文献
11.
V.B Headley 《Journal of Mathematical Analysis and Applications》1985,108(1):283-292
Let D(?) be the Doob's class containing all functions f(z) analytic in the unit disk Δ such that f(0) = 0 and lim on an arc A of ?Δ with length . It is first proved that if f?D(?) then the spherical norm ∥ f ∥ = supz?Δ, where C1 = limn→∞. Next, U represents the Seidel's class containing all non-constant functions f(z) bounded analytic in Δ such that almost everywhere. It is proved that inff?U∥f∥ = 0, and if f has either no singularities or only isolated singularities on ?Δ, then ∥f∥ ? C1. Finally, it is proved that if f is a function normal in Δ, namely, the norm ∥f∥< ∞, then we have the sharp estimate ∥fp∥ ? p∥f∥, for any positive integer p. 相似文献
12.
Louis de Branges 《Journal of Mathematical Analysis and Applications》1984,100(1):323-337
A fundamental problem is to estimate the logarithmic coefficients of a power series with constant coefficient zero which represents a function which has distinct values at distinct points of the unit disk. A source of estimates is an expansion theorem for the Löwner equations which is obtained from a study of contractive substitutions in Hilbert spaces of analytic functions. The methods are an outgrowth of the theory of square summable power series [1]. Assume that σn is a given function of nonnegative integers n, with nonnegative values, such that σ0 = 0 and such that σn ? 1 ? σn when n is positive. Infinite values are allowed. The underlying Hilbert space is the set σ(0) of equivalence classes of power series f(z) = ∑ anzn with constant coefficient zero such that f(z)2σ(0) = ∑(n/σn)|an|2 is finite. Equivalence of power series f(z) and g(z) means that the coefficient of zn in f(z) is equal to the coefficient of zn in g(z) when σn is finite. 相似文献
13.
We consider unique continuation theorems for solution of inequalities with W allowed to be unbounded. We obtain two kinds of results. One allows W ? Lploc(n) with . The other requires fW2 to be ?Δ-form bounded for all f ? C0∞. 相似文献
14.
The least absolute deviation estimates L(N), from N data points, of the autoregressive constants a = (a1, …, aq)′ for a stationary autoregressive model, are shown to have the property that Nσ(L(N) ? a) converge to zero in probability, for , where the disturbances are i.i.d., attracted to a stable law of index α, 1 ≤ α < 2, and satisfy some other conditions. 相似文献
15.
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
16.
17.
If A∈T(m, N), the real-valued N-linear functions on Em, and σ∈SN, the symmetric group on {…,N}, then we define the permutation operator Pσ: T(m, N) → T(m, N) such that Pσ(A)(x1,x2,…,xN = A(xσ(1),xσ(2),…, xσ(N)). Suppose Σqi=1ni = N, where the ni are positive integers. In this paper we present a condition on σ that is sufficient to guarantee that 〈Pσ(A1?A2???Aq),A1?A2?? ? Aq〉 ? 0 for Ai∈S(m, ni), where S(m, ni) denotes the subspace of T(m, ni) consisting of all the fully symmetric members of T(m, ni). Also we present a broad generalization of the Neuberger identity which is sometimes useful in answering questions of the type described below. Suppose G and H are subgroups of SN. We let TG(m, N) denote all A∈T(m, N) such that Pσ(A) = A for all σ∈G. We define the symmetrizer G: T(m, N)→TG(m,N) such that . Suppose H is a subgroup of G and A∈TH(m, N). Clearly We are interested in the reverse type of comparison. In particular, if D is a suitably chosen subset of TH(m,N), then can we explicitly present a constant C>0 such that for all A∈D? 相似文献
18.
Joel Anderson 《Journal of Functional Analysis》1979,31(2):195-217
Three main results are obtained: (1) If is an atomic maximal Abelian subalgebra of (), is the projection of () onto and h is a complex homomorphism on , then h ° is a pure state on (). (2) If {Pn} is a sequence of mutually orthogonal projections with rank(Pn) = n and ∑ Pn = I, is the projection of () onto {Pn}″ given by P(T)=∑tracen(T)Pn and h is a homomorphism on {Pn}″ such that h(Pn) = 0 for all n then h ° induces a type II∞ factor representation of the Calkin algebra. (3) If is a nonatomic maximal Abelian subalgebra of () then there is an atomic maximal Abelian subalgebra of () and a large family {Φα} of 1-homomorphisms from onto such that for each α, Φα ° is an extreme point in the set of projections from () onto . (Here denotes the projection of () onto .) 相似文献
19.
Pierrette Cassou-Noguès 《Journal of Number Theory》1982,14(1):32-64
In this paper, we are studying Dirichlet series Z(P,ξ,s) = Σn?1rP(n)?s ξn, where P ∈ + [X1,…,Xr] and ξn = ξ1n1 … ξrnr, with ξi ∈ , such that |ξi| = 1 and ξi ≠ 1, 1 ≦ i ≦ r. We show that Z(P, ξ,·) can be continued holomorphically to the whole complex plane, and that the values Z(P, ξ, ?k) for all non negative integers, belong to the field generated over by the ξi and the coefficients of P. If, there exists a number field K, containing the ξi, 1 ≦ i ≦ r, and the coefficients of P, then we study the denominators of Z(P, ξ, ?k) and we define a -adic function Z(P, ξ,·) which is equal, on class of negative integers, to Z(P, ξ, ?k). 相似文献
20.
E.B Dynkin 《Journal of Functional Analysis》1985,62(3):397-434
Let Xt be the Brownian motion in d. The random set Γ = {(t1,…, tn, z): Xtl = ··· = Xtn = z} in d + n is empty a.s. except in the following cases: (a) n = 1, d = 1, 2,…; (b) d = 2, n = 2, 3,…; (c) d = 3, n = 2. In each of these cases, a family of random measures Mλ concentrated on Γ is constructed (λ takes values in a certain class of measures on d). Measures Mλ characterize the time-space location of self-intersections for Brownian paths. If n = d = 1, then Mλ(dt, dz) = λ(dz) Nz(dt) where N2 is the local time at z. In the case n = 2, the set Γ can be identified with the set of Brownian loops. The measure Mλ “explodes” on the diagonal {t1 = t2} and, to study small loops, a random distribution which regularizes Mλ is constructed. 相似文献