共查询到20条相似文献,搜索用时 156 毫秒
1.
If T is an n × n matrix with nonnegative integral entries, we define a transformation T: Cn → Cn by w = Tz where We consider functions f(z) of n complex variables which satisfy a functional equation giving f(Tz) as a rational function of 1f(z) and we obtain conditions under which such a function f(z) takes transcendental values at algebraic points. 相似文献
2.
Hans G Kaper 《Journal of Mathematical Analysis and Applications》1977,59(3):415-422
In this paper the integrals are investigated for positive real values of the variable τ. Here, m is a nonnegative integer, v is a complex variable with Re(v) > ?1. Both integrals are related to the complex integral Φmγ(z) = ∝0∞exp[?(t ? z)]t?γ(ln t)m(t ? z)?1dt with 0 ? Re(γ) < 1, the behavior of which is analyzed in detail. The results are applied to obtain asymptotic representations for fmn(τ) and gmn(τ), m and n both nonnegative integers, near τ = 0. The latter integrals play a role in the study of the equations of neutron transport and radiative transfer. 相似文献
3.
Jorge L.C Sanz Thomas S Huang 《Journal of Mathematical Analysis and Applications》1984,104(1):302-308
In this paper, the problem of phase reconstruction from magnitude of multidimensional band-limited functions is considered. It is shown that any irreducible band-limited function f(z1…,zn), zi ? , i=1, …, n, is uniquely determined from the magnitude of f(x1…,xn): | f(x1…,xn)|, xi ? , i=1,…, n, except for (1) linear shifts: i(α1z1+…+αn2n+β), β, αi?, i=1,…, n; and (2) conjugation: . 相似文献
4.
n independent adiabatic invariants in involution are found for a slowly varying Hamiltonian system of order 2n × 2n. The Hamiltonian system considered is , where A(t) is a 2n × 2n real matrix with distinct, pure imaginary eigen values for each t? [?∞, ∞], and , for all j > 0. The adiabatic invariants Is(u, t), s = 1,…, n are expressed in terms of the eigen vectors of A(t). Approximate solutions for the system to arbitrary order of ? are obtained uniformly for t? [?∞, ∞]. 相似文献
5.
Results on partition of energy and on energy decay are derived for solutions of the Cauchy problem . Here the Aj's are constant, k × k Hermitian matrices, x = (x1,…, xn), t represents time, and u = u(t, x) is a k-vector. It is shown that the energy of Mu approaches a limit , where M is an arbitrary matrix; that there exists a sufficiently large subspace of data ?, which is invariant under the solution group U0(t) and such that depending on ? and that the local energy of nonstatic solutions decays as . More refined results on energy decay are also given and the existence of wave operators is established, considering a perturbed equation at infinity. 相似文献
6.
Carlo Sbordone 《Comptes Rendus Mathematique》2003,337(3):165-170
Adjugate Jacobians of mappings can be represented in terms of Jacobian matrices: , for , by mean of symmetric matrix fields with a.e. Under suitable conditions, we prove that weakly in if and only if Γ-converges to a matrix with satisfying . To cite this article: C. Sbordone, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
7.
This paper deals with asymptotic behavior for (weak) solutions of the equation , on + × Ω; u(t, x) = 0, on + × ?Ω. If and β is coercive, we prove that the solutions are bounded in the energy space, under weaker assumptions than those used by G. Prouse in a previous work. If in addition and ? is srongly almost-periodic, we prove for strongly monotone β that all solutions are asymptotically almost-periodic in the energy space. The assumptions made on β are much less restrictive than those made by G. Prouse: mainly, we allow β to be multivalued, and in the one-dimensional case β need not be defined everywhere. 相似文献
8.
Wolfgang Wasow 《Linear algebra and its applications》1977,18(2):163-170
Let A(x,ε) be an n×n matrix function holomorphic for |x|?x0, 0<ε?ε0, and possessing, uniformly in x, an asymptotic expansion , as ε→0+. An invertible, holomorphic matrix function P(x,ε) with an asymptotic expansion , as ε→0+, is constructed, such that the transformation y = P(x,ε)z takes the differential equation a positive integer, into , where B(x,ε) is asymptotically equal, to all orders, to a matrix in a canonical form for holomorphic matrices due to V.I. Arnold. 相似文献
9.
Let (Wt) = (W1t,W2t,…,Wdt), d ? 2, be a d-dimensional standard Brownian motion and let A(t) be a bounded measurable function from + into the space of d × d skew-symmetric matrices and x(t) such a function into d. A class of stochastic processes (LtA,x), a particular example of which is Levy's “stochastic area” , is dealt with.The joint characteristic function of Wt and L1A,x is calculated and based on this result a formula for fundamental solutions for the hypoelliptic operators which generate the diffusions (Wt,LtA,x) is given. 相似文献
10.
We are interested in the parallel computation of a linear mapping of n real variables by a network of computers with restricted means of communication between them and without any common memory. Let denote the algebra of n×n real matrices, and let G be the graph associated with a binary, reflexive and symmetric relation R over {1,2, …,n}. We define A matrix is said to be realizable on G if it can be expressed as a product of elements of AR. Therefore, every matrix of is realizable on G if and only if AR generates . We show that AR generates if and only if G is connected. 相似文献
11.
Necessary and sufficient conditions for a solution {zk} of the difference equation , with singular, to be a convergent sequence of vectors are given under a variety of assumptions. Theoretical results on iterative schemes for solving Ax = b by singular splittings, , are given first. In particular, the case when and is positive semi-definite is considered. Then applications to discrete control problems and backwards population projection are discussed. 相似文献
12.
Robert Donaghey 《Journal of Combinatorial Theory, Series A》1980,28(1):111-114
For a formal power series with nonnegative integer coefficients, the compositional inverse of is shown to be the generating function for the colored planted plane trees in which each vertex of degree i + 1 is colored one of hi colors. Since the compositional inverse of the Euler transformation of f(t) is the star transformation [[g(t)]?1 ? 1]?1 of g(t), [2], it follows that the Euler transformation of f(t) is the generating function for the colored planted plane trees in which each internal vertex of degree i + 1 is colored one of hi colors for i > 1, and h1 ? 1 colors for i = 1. 相似文献
13.
Tomas Schonbek 《Journal of Differential Equations》1985,56(2):290-296
New and more elementary proofs are given of two results due to W. Littman: (1) Let . The estimate cannot hold for all u?C0∞(Q), Q a cube in , some constant C. (2) Let n ? 2, p ≠ 2. The estimate cannot hold for all C∞ solutions of the wave equation □u = 0 in ; all t ?; some function C: → . 相似文献
14.
The integral transform , where α and β are real, of pairs of special analytic functions f(z) = z + ···, g(z) = z + ···, univalent in the open unit disc Δ is studied. The transform and our results extend some recent results due to Shirakova. 相似文献
15.
Charles Rennolet 《Journal of Mathematical Analysis and Applications》1979,70(1):42-60
Existence and boundedness theorems are given for solutions of nonlinear integrodifferential equations of type , (1.1) u(0) = u0, Here A and B are nonlinear, possibly multivalued, operators on a Banach space W and a Hilbert space H, where W ? H. The function f (0, ∞) → H and the kernel a(t, s): × → are known functions. The results of this paper extend the results of Crandall, Londen, and Nohel [4] for equation (1.1). They assumed the kernel to be of the type a(t, s) = a(t ? s). We relax this assumption and obtain similar results. Examples of kernels satisfying the conditions we require are given in section 4. 相似文献
16.
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
17.
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
18.
Let A be an arbitrary n×n matrix, partitioned so that if A=[Aij], then all submatrices Aii are square. If x is a positive vector, it is well-known that , where , contains all the eigenvalues of A. The purpose of this paper is to give a new definition of the concept of an isolated subregion of G(x). An algorithm is given for obtaining the best such isolated subregion in a certain sense, and examples are given to show that tighter bounds for some eigenvalues of A may be obtained than with previous algorithms. For ease of computation, each subregion Gi(x) is replaced by the union of circular disks centered at the eigenvalues of Aii. 相似文献
19.
A regularity result for singular nonlinear elliptic systems in inverse-power weighted Sobolev spaces
P.D Smith 《Journal of Differential Equations》1984,53(2):125-138
The compactness method to weighted spaces is extended to prove the following theorem:Let H2,s1(B1) be the weighted Sobolev space on the unit ball in Rn with norm Let n ? 2 ? s < n. Let u? [H2,s1(B1) ∩ L∞(B1)]N be a solution of the nonlinear elliptic system , are uniformly continuous functions of their arguments and satisfy: . Then there exists an R1, 0 < R1 < 1, and an α, 0 < α < 1, along with a set such that (1) , (2) Ω does not contain the origin; Ω does not contain BR1, (3) is open, (4) u is ; u is LipαBR1. 相似文献
20.
S. Ihara 《Journal of multivariate analysis》1974,4(1):74-87
The message m = {m(t)} is a Gaussian process that is to be transmitted through the white Gaussian channel with feedback: . Under the average power constraint, , we construct causally the optimal coding, in the sense that the mutual information It(m, Y) between the message m and the channel output Y (up to t) is maximized. The optimal coding is presented by , where and A(s) is a positive function such that . 相似文献