共查询到20条相似文献,搜索用时 31 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.
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
4.
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
5.
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
6.
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
7.
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
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.
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
14.
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
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.
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
18.
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
19.
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
20.
Derek W Robinson 《Journal of Functional Analysis》1977,24(3):280-290
Let U, V be two strongly continuous one-parameter groups of bounded operators on a Banach space with corresponding infinitesimal generators S, T. We prove the following: ∥Ut, ? Vt ∥ = O(t), t → 0, if and only if U = V; ∥Ut ? Vt∥ = O(tα), t → 0; with 0 ? α ? 1, if and only if , where Ω, P, are bounded operators on such that if and only if has a bounded extension to 1. Further results of this nature are inferred for semigroups, reflexive spaces, Hilbert spaces, and von Neumann algebras. 相似文献