共查询到20条相似文献,搜索用时 31 毫秒
1.
Allan M Krall 《Journal of Differential Equations》1977,24(2):253-267
This article discusses linear differential boundary systems, which include nth-order differential boundary relations as a special case, in np[0,1] × np[0,1], 1 ? p < ∞. The adjoint relation in nq[0,1] × nq[0,1], , is derived. Green's formula is also found. Self-adjoint relations are found in n2[0,1] × n2[0,1], and their connection with Coddington's extensions of symmetric operators on subspaces of np[0,1] × n2[0,1] is established. 相似文献
2.
Misha Zafran 《Journal of Functional Analysis》1977,26(3):289-314
Let 1 < p < ∞ with p ≠ 2. Let G denote one of the groups n, n, or n. We show that only entire functions operate in certain algebras of multipliers on Lp(G). 相似文献
3.
Yoshiyuki Kitaoka 《Journal of Number Theory》1980,12(2):224-229
Let L be a positive Z-lattice with level N = cd, (c, d) = 1. Then the Fourier expansion at cusp of the theta function associated to L is a theta function associated to L1, where a lattice L1 is defined by ZpL1 = ZpL for , ZpL1 = the dual of ZpL for p | c. 相似文献
4.
Following the lines of [13] we introduce the classes of mixed smoothness αp(Rn), αp(Zn) for a multi-index α = (α1,…, αn). Such classes are naturally tied up with the study of semi-elliptic differential and difference equations.Besides a brief presentation of such classes, we concentrate our research on the study of mixed homogeneous multipliers with homogeneity β = (β1, …, βn) and their preservation of mixed homogeneous Hölder classes α∞, for a different multi-index α.In the last paragraph we apply the results to produce various improvements of the classical Schauder's estimates, for differential and difference equations, in the parabolic and elliptic case. 相似文献
5.
Given an embedding f: G →2 of a graph G in the two-dimensional lattice, let |f| be the maximum L1 distance between points f(x) and f(y) where xy is an edge of G. Let B2(G) be the minimum |f| over all embeddings f. It is shown that the determination of B2(G) for arbitrary G is NP-complete. Essentially the same proof can be used in showing the NP-completeness of minimizing |f| over all embeddings f: G → n of G into the n-dimensional integer lattice for any fixed n ≥ 2. 相似文献
6.
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
7.
James D Child 《Journal of Mathematical Analysis and Applications》1980,78(1):133-143
Let Ω denote a simply connected domain in the complex plane and let be the collection of all entire functions of exponential type whose Laplace transforms are analytic on Ω′, the complement of Ω with respect to the sphere. Define a sequence of functionals by , where F denotes the Laplace transform of f, Γ ? Ω is a simple closed contour chosen so that F is analytic outside and on Ω, and gn is analytic on Ω. The specific functionals considered by this paper are patterned after the Lidstone functions, L2n(f) = f(2n)(0) and L2n + 1(f) = f(2n)(1), in that their sequence of generating functions {gn} are “periodic.” Set gpn + k(ζ) = hk(ζ) ζpn, where p is a positive integer and each hk (k = 0, 1,…, p ? 1) is analytic on Ω. We find necessary and sufficient conditions for . DeMar previously was able to find necessary conditions [7]. Next, we generalize {Ln} in several ways and find corresponding necessary and sufficient conditions. 相似文献
8.
Rainer Schulze-Pillot 《Journal of Number Theory》1982,14(2):237-250
We study the representation behaviour of a -lattice L on a positive definite ternary quadratic space V over . As a new tool for this we use the Bruhat-Tits building of the spingroup of the completion of V at a suitable prime p. In Section 2 we show how this can be described in an elementary way as a graph whose vertices are the p-maximal lattices on Vp, and in Section 4 we let this graph induce a graph, whose vertices are lattices on V, which differ from L only at the prime p. In Section 3 we investigate which lattices from the graph defined in Section 2 have a given vector in common. The results are used in Sections 5 and 6 to obtain information on the representation behaviour of some special lattices. In Section 5 we get a list of lattices, which represent all numbers they represent locally everywhere; this list contains that given by Watson in [16]. In Section 6 we sharpen a result of Jones and Pall from [6]. 相似文献
9.
Z.A Karian 《Journal of Number Theory》1976,8(2):233-244
Let k be a positive square free integer, the ring of algebraic integers in and S the unit sphere in Cn, complex n-space. If A1,…, An are n linearly independent points of Cn then L = {u1Au + … + unAn} with is called a k-lattice. The determinant of L is denoted by d(L). If L is a covering lattice for S, then is the covering density. L is called locally (absolutely) extreme if θ(S, L) is a local (absolute) minimum. In this paper we determine unique classes of extreme lattices for k = 1 and k = 3. 相似文献
10.
11.
Hendrik S.V de Snoo 《Journal of Mathematical Analysis and Applications》1983,92(1):172-179
With an ordinary differential expression L = ∑nk=0PkDk on an open interval I? is associated a selfadjoint operator H in a Hilbert space, possibly beyond =L2(l). The set H∩ only depends on the generalized spectral family associated with H. It is shown that the (differentiated) eigenfunction expansion given by H converges uniformly on compact subintervals of l for functions in (H)∩ In case H is a semibounded selfadjoint operator in =L2T, a similar result is proved for functions in |H|, which is the set of all ∈ for which there exists a sequence fn∈(H) such that fn→f in and (H(fn ? fm), fn ? fm → 0 as n, m → ∞. 相似文献
12.
Marvin I. Knopp 《Journal of Number Theory》1980,12(1):2-9
If h, k ∈ Z, k > 0, the Dedekind sum is given by , with , . The Hecke operators Tn for the full modular group SL(2, Z) are applied to log η(τ) to derive the identities (n ∈ Z+) , where (h, k) = 1, k > 0 and σ(n) is the sum of the positive divisors of n. Petersson had earlier proved (1) under the additional assumption k ≡ 0, h ≡ 1 (mod n). Dedekind himself proved (1) when n is prime. 相似文献
13.
Jin Bai Kim 《Linear algebra and its applications》1975,10(1):69-70
Let L(E) be the set of all linear mappings of a vector space E. Let Z+ be the set of all positive integers. A nonzero element ? in L(E) is called an r-potent if . We prove that is a semigroup generated by the set of all r-potents in S(E), where r is a fixed positive integer with 2?r?n=dim(E). 相似文献
14.
Jean Bourgain 《Comptes Rendus Mathematique》2002,335(6):529-531
We consider quasi-periodic Schrödinger operators H on of the form H=Hλ,x,ω=λv(x+nω)δn,n′+Δ where v is a non-constant real analytic function on the d-torus and Δ denotes the discrete lattice Laplacian on . Denote by Lω(E) the Lyapounov exponent, considered as function of the energy E and the rotation vector . It is shown that for |λ|>λ0(v), there is the uniform minoration for all E and ω. For all λ and ω, Lω(E) is a continuous function of E. Moreover, Lω(E) is jointly continuous in (ω,E), at any point such that k·ω0≠0 for all . To cite this article: J. Bourgain, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 529–531. 相似文献
15.
S.M. Gersten 《Journal of Pure and Applied Algebra》1984,33(3):269-279
A presentation is given for SAn, the group of automorphisms of determinant 1 of a free group Fn of rank n. The canonical isomorphisms are established for n ≥ 5, where An is the full group of automorphisms of Fn. 相似文献
16.
《Journal of Functional Analysis》1987,73(1):122-134
Let Ω denote a connected and open subset of n. The existence of n commuting self-adjoint operators H1,…, Hn on such that each Hj is an extension of (acting on is shown to be equivalent to the existence of a measure μ on n such that f → tf (the Fourier transform of f) is unitary from onto Ω. It is shown that the support of μ can be chosen as a subgroup of n iff H1,…, Hn can be chosen such that the unitary groups generated by H1,…, Hn act multiplicatively on . This happens iff Ω (after correction by a null set) forms a system of representatives for the quotient of n by some subgroup, i.e., iff Ω is essentially a fundamental domain. 相似文献
17.
18.
Palle E.T. Jørgensen 《Advances in Mathematics》1982,44(2):105-120
Let Ω be an arbitrary open subset of n of finite positive measure, and assume the existence of a subset Λ ? n such that the exponential functions eλ = exp i(λ1x1 + … + λnxn), λ = (λ1,…, λn) ∈ Λ, form an orthonormal basis for with normalized measure. Assume 0 ∈ Λ and define subgroups K and A of (n, +) by K = Λ0 = {γ ∈ n:γ·λ ∈ 2π}, A = {a ∈ n:Ua U1a = }, where Ut is the unitary representation of n on given by Ute = eitλeλ, t ∈ n, λ ∈ Λ, and where is the multiplication algebra of on L2. Assume that A is discrete. Then there is a discrete subgroup D ? A of dimension n, a fundamental domain for D, and finite sets of representers RΛ, RΓ, , each containing 0, RΛ for in K0, and for in A such that Ω is disjoint union of translates of : Ω = ∪a∈RΩ (a + ), neglecting null sets, and Λ = RΛ ⊕ D0. If RΓ is a set of representers for in D, then Γ = RΓ ⊕ K is a translation set for Ω, i.e., Ω ⊕ Γ = n, direct sum, (neglecting null sets). The case A = n corresponds to Ω = , Λ = D0 and Γ = K. This last case corresponds in turn to a function theoretic assumption of Forelli. 相似文献
19.
Given an integer k>0, our main result states that the sequence of orders of the groups (respectively, of the groups ) is Cesàro equivalent as n→∞ to the sequence C1(k)nk2?1 (respectively, C2(k)nk2), where the coefficients C1(k) and C2(k) depend only on k; we give explicit formulas for C1(k) and C2(k). This result generalizes the theorem (which was first published by I. Schoenberg) that says that the Euler function ?(n) is Cesàro equivalent to . We present some experimental facts related to the main result. To cite this article: A.G. Gorinov, S.V. Shadchin, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
20.
Let M be an n-dimensional manifold supporting a quasi-Anosov diffeomorphism. If n=3 then either , in which case the diffeomorphisms is Anosov, or else its fundamental group contains a copy of . If n=4 then Π1(M) contains a copy of , provided that the diffeomorphism is not Anosov. To cite this article: J. Rodriguez Hertz et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 321–323. 相似文献