共查询到20条相似文献,搜索用时 62 毫秒
1.
Jeffrey Rauch 《Journal of Functional Analysis》1980,35(3):304-315
Suppose that e2?|x|V ∈ ReLP(R3) for some p > 2 and for g ∈ R, H(g) = ? Δ + gV, H(g) = ?Δ + gV. The main result, Theorem 3, uses Puiseaux expansions of the eigenvalues and resonances of H(g) to study the behavior of eigenvalues λ(g) as they are absorbed by the continuous spectrum, that is . We find a series expansion in powers of whose values for g < g0 correspond to resonances near the origin. These resonances can be viewed as the traces left by the just absorbed eigenvalues. 相似文献
2.
Douglas Hensley 《Journal of Number Theory》1977,9(4):510-524
A factorial set for the Gaussian integers is a set G = {g1, g2 … gn} of Gaussian integers such that takes Gaussian integer values at Gaussian integers. We characterize factorial sets and give a lower bound for . It is conjectured that there are infinitely many factorial sets. A Gaussian integer valued polynomial (GIP) is a polynomial with the title property. A bound similar to the above is given for max∥z∥2=n ∥ G(z)∥ if G(z) is a GIP. There is a relation between factorial sets and testing for GIP's. We discuss this and close with some examples of factorial sets, and speculate on how to find more. 相似文献
3.
The group ring R(G) of a group G over a coefficient ring R is well known and so is the L1 group algebra . We study in this note . where R is Zp(Qp) the ring (field) of p-adic integers (numbers) equipped with the p-adic valuation. Analogues of certain well known results for group rings and l1(G) are obtained for l(R,G). 相似文献
4.
5.
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
6.
This paper is a study of the distribution of eigenvalues of various classes of operators. In Section 1 we prove that the eigenvalues (λn(T)) of a p-absolutely summing operator, p ? 2, satisfy This solves a problem of A. Pietsch. We give applications of this to integral operators in Lp-spaces, weakly singular operators, and matrix inequalities.In Section 2 we introduce the quasinormed ideal Π2(n), P = (p1, …, pn) and show that for T ∈ Π2(n), 2 = (2, …, 2) ∈ Nn, the eigenvalues of T satisfy More generally, we show that for T ∈ Πp(n), P = (p1, …, pn), pi ? 2, the eigenvalues are absolutely p-summable, We also consider the distribution of eigenvalues of p-nuclear operators on Lr-spaces.In Section 3 we prove the Banach space analog of the classical Weyl inequality, namely , 0 < p < ∞, where αn denotes the Kolmogoroff, Gelfand of approximation numbers of the operator T. This solves a problem of Markus-Macaev.Finally we prove that Hilbert space is (isomorphically) the only Banach space X with the property that nuclear operators on X have absolutely summable eigenvalues. Using this result we show that if the nuclear operators on X are of type l1 then X must be a Hilbert space. 相似文献
7.
J.S. Hwang 《Journal of Mathematical Analysis and Applications》1983,91(2):434-443
For any fixed 0 < π ? 2π, let D(π) be the family of all holomorphic functions in the unit disk Δ which satisfy (i)f(0) = 0 and (ii) , for all π lying on some arc Af ? ?Δ with arclength . We show that for each 0 < ε < 1, there is a π0 > 0 such that for any f?D(π) with π < π0, the Bloch and Doob norm respectively satisfy These two estimates do not hold with ε = 0. 相似文献
8.
Tom Brylawski 《Discrete Mathematics》1977,18(3):243-252
In “The Slimmest Geometric Lattices” (Trans. Amer. Math. Soc.). Dowling and Wilson showed that if G is a combinatorial geometry of rank r(G) = n, and if X(G) = Σμ(0, x)λr ? r(x) = Σ (?1)r ? kWkλk is the characteristic polynomial of G, then Thus γ(G) ? 2r ? 1 (n+2), where γ(G) = Σwk. In this paper we sharpen these lower bounds for connected geometries: If G is connected, r(G) ? 3, and n(G) ? 2 ((r, n) ≠ (4,3)), then |μ| ? (r? 1)n; and γ ? (2r ? 1 ? 1)(2n + 2). These bounds are all achieved for the parallel connection of an r-point circuit and an (n + 1)point line. If G is any series-parallel network, , and then . Further, if β is the Crapo invariant, then β(G) ? max(1, n ? r + 2). This lower bound is achieved by the parallel connection of a line and a maximal size series-parallel network. 相似文献
9.
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
10.
Arthur Lubin 《Journal of Functional Analysis》1974,17(4):388-394
Let m and vt, 0 ? t ? 2π be measures on T = [0, 2π] with m smooth. Consider the direct integral = ⊕L2(vt) dm(t) and the operator on , where e(s, t) = exp ∫st ∫Tdvλ(θ) dm(λ). Let μt be the measure defined by for all continuous ?, and let ?t(z) = exp[?∫ (eiθ + z)(eiθ ? z)?1dμt(gq)]. Call {vt} regular iff for all for 1 a.e. 相似文献
11.
R Lowen 《Journal of Mathematical Analysis and Applications》1978,64(2):446-454
Starting from a defining differential equation of the kernel of an exponential operator with normalization ∫?∞∞W(λ, t, u) du = 1, we determine Sλ for various p(t) including; for example, p(t) a quadratic polynomial, all the known exponential operators are recovered and some new ones are constructed. It is shown that all the exponential operators are approximation operators. Further approximation properties of these operators are discussed. For example, functions satisfying are characterized. Several results of C. P. May are also improved. 相似文献
12.
Hans G Weidner 《Journal of Number Theory》1976,8(1):99-108
Let g = (g1,…,gr) ≥ 0 and h = (h1,…,hr) ≥ 0, g?, h? ∈ , be two vectors of nonnegative integers and let λ ? , λ ≥ 0, λ ≡ 0 mod d, where d denotes g.c.d. (g1,…,gr). Define It is shown in this paper that Λ(λ) is periodic in λ with constant jump. If i? {1,…,r} is such that then holds true for all sufficiently large λ, λ ≡ 0 mod d. 相似文献
13.
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
14.
Steven Zelditch 《Journal of Functional Analysis》1983,50(1):67-80
We prove a Szegö-type theorem for some Schrödinger operators of the form with V smooth, positive and growing like . Namely, let πλ be the orthogonal projection of L2 onto the space of the eigenfunctions of H with eigenvalue ?λ; let A be a 0th order self-adjoint pseudo-differential operator relative to Beals-Fefferman weights and with total symbol a(x, ξ); and let f∈C(). Then (assuming one limit exists). 相似文献
15.
Douglas N. Clark 《Journal of Functional Analysis》1973,14(3):269-280
The operator acting on H=∝02π⊕L2(vt), where m and vt, 0 ? t ? 2π are measures on [0, 2π] with m smooth and e(s, t) = exp[?∝ts∝Tdvλ(θ) dm(λ)], satisfies . It is, therefore, unitarily equivalent to a scalar Sz.-Nagy-Foia? canonical model. The purpose of this paper is to determine the model explicitly and to give a formula for the unitary equivalence. 相似文献
16.
CAI Mao-cheng 《Discrete Mathematics》1984,49(1):15-20
Given a finite loopless graph G (resp. digraph D), let σ(G), ?(G) and ψ(D) denote the minimal cardinalities of a completely separating system of G, a separating system of G and a separating system of D, respectively. The main results of this paper are: denotes the chromatic number of G. (ii) All the problems of determining σ(G), ?(G) and ψ(D) are NP-complete. 相似文献
17.
Joachim Mahnkopf 《Comptes Rendus Mathematique》2004,338(10):759-762
Let π be a cuspidal representation of with non-vanishing cohomology and denote by L(π,s) its L-function. Under a certain local non-vanishing assumption, we prove the rationality of the values of L(π?χ,0) for characters χ, which are critical for π. Note that conjecturally any motivic L-function should coincide with an automorphic L-function on GLn; hence, our result corresponds to a conjecture of Deligne for motivic L-functions. To cite this article: J. Mahnkopf, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
18.
Let Π(G) be the set of paths of a particular class Π from the initial to the terminal root of a two-rooted (possibly directed) graph G. We consider the family of -weights defined by where Πx(G) is the family of subsets of Π(G) which cover x(G), the vertex set or the edge (arc) set of G.A number of the common properties and interrelations of these weights are discussed. Some of the weights have been considered previously, [1, 2], in the context of percolation theory but here only combinatorial arguments are used. 相似文献
19.
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