共查询到20条相似文献,搜索用时 15 毫秒
1.
R.J. Williams 《Advances in Applied Mathematics》1985,6(1):1-3
Let {Xt, t ≥ 0} be Brownian motion in d (d ≥ 1). Let D be a bounded domain in d with C2 boundary, ?D, and let q be a continuous (if d = 1), Hölder continuous (if d ≥ 2) function in D?. If the Feynman-Kac “gauge” Ex{exp(∝0τDq(Xt)dt)1A(XτD)}, where τD is the first exit time from D, is finite for some non-empty open set A on ?D and some x?D, then for any ), is the unique solution in of the Schrödinger boundary value problem . 相似文献
2.
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
3.
M.P Heble 《Journal of Mathematical Analysis and Applications》1983,93(2):363-384
Given a cocycle a(t) of a unitary group {U1}, ?∞ < t < ∞, on a Hilbert space , such that a(t) is of bounded variation on [O, T] for every T > O, a(t) is decomposed as a(t) = f;t0Usxds + β(t) for a unique x ? , β(t) yielding a vector measure singular with respect to Lebesgue measure. The variance is defined as if existing. For a stationary diffusion process on 1, with Ω1, the space of paths which are natural extensions backwards in time, of paths confined to one nonsingular interval J of positive recurrent type, an information function I(ω) is defined on , based on the paths restricted to the time interval [0, 1]. It is shown that is continuous and bounded on . The shift τt, defines a unitary representation {Ut}. Assuming , dm being the stationary measure defined by the transition probabilities and the invariant measure on J, has a C∞ spectral density function f;. It is then shown that σ2({Ut}, I) = f;(O). 相似文献
4.
We construct two d-dimensional independent diffusions , with the same viscosity ν≠0 and the same drift u(x,t)=(pρta(x)v1+(1?p)ρtb(x)v2)/(pρta(x)+(1?p)ρtb(x)), where ρta,ρtb are respectively the density of Xta and Xtb. Here and p∈(0,1) are given. We show that is the unique weak solution of the following pressureless gas system such that as t→0+. To cite this article: A. Dermoune, S. Filali, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
5.
Let Ω be a simply connected domain in the complex plane, and , the space of functions which are defined and analytic on , if K is the operator on elements defined in terms of the kernels ki(t, s, a1, …, an) in by is the identity operator on , then the operator I ? K may be factored in the form (I ? K)(M ? W) = (I ? ΠK)(M ? ΠW). Here, W is an operator on defined in terms of a kernel w(t, s, a1, …, an) in by Wu = ∝antw(t, s, a1, …, an) u(s, a1, …, an) ds. ΠW is the operator; ΠWu = ∝an ? 1w(t, s, a1, …, an) u(s, a1, …, an) ds. ΠK is the operator; ΠKu = ∑i = 1n ? 1 ∝aitki(t, s, a1, …, an) ds + ∝an ? 1tkn(t, s, a1, …, an) u(s, a1, …, an) ds. The operator M is of the form m(t, a1, …, an)I, where and maps elements of into itself by multiplication. The function m is uniquely derived from K in the following manner. The operator K defines an operator on functions u in , by . A determinant of the operator is defined as an element of . This is mapped into by setting an + 1 = t to give m(t, a1, …, an). The operator I ? ΠK may be factored in similar fashion, giving rise to a chain factorization of I ? K. In some cases all the matrix kernels ki defining K are separable in the sense that ki(t, s, a1, …, an) = Pi(t, a1, …, an) Qi(s, a1, …, an), where Pi is a 1 × pi matrix and Qi is a pi × 1 matrix, each with elements in , explicit formulas are given for the kernels of the factors W. The various results are stated in a form allowing immediate extension to the vector-matrix case. 相似文献
6.
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
7.
Peter Wolfe 《Journal of Functional Analysis》1980,36(1):105-113
Let Lu be the integral operator defined by where S is the interior of a smooth, closed Jordan curve in the plane, k is a complex number with Re k ? 0, Im k ? 0, and ?2 = (x ?x′)2 + (y ? y′)2. We define , where in the definition of W21(q, S) the derivatives are taken in the sense of distributions. We prove that Lk is a continuous 1-l mapping of L2(q, S) onto W21(q, S). 相似文献
8.
Si studia, in un cilindro, il problema di Dirichlet per l'equazione ellittica del II ordine: , dove è l'operatore a coefficienti discontinui sull'asse x3 già introdotto da N. Ural'tseva per mostrare che l'equazione considerata può non avere soluzione nello spazio di Sobolev W2,p(p > 2) per qualche f?Lp. In questo lavoro si danno limitazioni a priori e teoremi di esistenza e unicità in W2,p quando p varia in un intervallo (p1(α), p2(α)), dipendente dalla costante di ellitticità α. Se p = p2(α) le limitazioni a priori cadono: l'esempio è quello di Ural'tseva. 相似文献
9.
In this paper, we establish the following results: Let A be a square matrix of rank r. Then (a) is idempotent of rank r, and trrA (defined as the sum of the principal minors of order r in A) is one iff A is Hermitian idempotent. (b) As=At for some positive integers s≠t, and trA=rankA iff A is idempotent. (c) for some integers s≠t iff is idempotent, while for some integers s≠0 iff . (d) for some integers s≠t and rankA=trA iff A is Hermitian idempotent, while for some integer s iff A is Hermitian. Here indicates the conjugate transpose of A, and P-α is defined iff (P+)α=(Pα)+ for all positive integers α and P+ is the Moore-Penrose inverse of P. 相似文献
10.
The notion of naturalness for L1-processes over a probability gage space is defined and the uniqueness of Doob decompositions of supermartingales is discussed. In particular, it is shown that if (Xt) is an Itô-Clifford stochastic integral martingale, then () has a unique decomposition into the sum of an L1-martingale and an increasing L1-process null at t = 0. 相似文献
11.
12.
13.
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
14.
Ep de Jonge 《Journal of Functional Analysis》1976,23(2):119-134
Under the condition that , (the set of singular functionals on a normed Köthe space Lθ) is an abstract L-space, it is proved in this paper that there exists a set of purely finitely additive measures θ such that ? holds. It follows that is an abstract L-space if and only if is Riesz isomorphic and isometric with a band in . 相似文献
15.
David S. Jerison 《Journal of Functional Analysis》1981,43(2):224-257
Let L = ∑j = 1mXj2 be sum of squares of vector fields in n satisfying a Hörmander condition of order 2: span{Xj, [Xi, Xj]} is the full tangent space at each point. A point x??D of a smooth domain D is characteristic if X1,…, Xm are all tangent to ?D at x. We prove sharp estimates in non-isotropic Lipschitz classes for the Dirichlet problem near (generic) isolated characteristic points in two special cases: (a) The Grushin operator in 2. (b) The real part of the Kohn Laplacian on the Heisenberg group in 2n + 1. In contrast to non-characteristic points, C∞ regularity may fail at a characteristic point. The precise order of regularity depends on the shape of ?D at x. 相似文献
16.
J.H Michael 《Journal of Mathematical Analysis and Applications》1981,79(1):203-217
We consider the mixed boundary value problem , where Ω is a bounded open subset of n whose boundary Γ is divided into disjoint open subsets Γ+ and Γ? by an (n ? 2)-dimensional manifold ω in Γ. We assume A is a properly elliptic second order partial differential operator on and Bj, for j = 0, 1, is a normal jth order boundary operator satisfying the complementing condition with respect to A on . The coefficients of the operators and Γ+, Γ? and ω are all assumed arbitrarily smooth. As announced in [Bull. Amer. Math. Soc.83 (1977), 391–393] we obtain necessary and sufficient conditions in terms of the coefficients of the operators for the mixed boundary value problem to be well posed in Sobolev spaces. In fact, we construct an open subset of the reals such that, if then for is a Fredholm operator if and only if s ∈ . Moreover, = ?xewx, where the sets x are determined algebraically by the coefficients of the operators at x. If n = 2, x is the set of all reals not congruent (modulo 1) to some exceptional value; if n = 3, x is either an open interval of length 1 or is empty; and finally, if n ? 4, x is an open interval of length 1. 相似文献
17.
Václav E. Beneš 《Stochastic Processes and their Applications》1974,2(2):127-140
Girsanov's theorem is a generalization of the Cameron-Martin formula for the derivative of a measure induced by a translation in Wiener space. It states that for ? a nonanticipative Brownian functional with ∫|?|2 ds < ∞ a.s. and with , where , the translated functions are a Wiener process under P?. The Girsanov functionals exp [ζ(?)] have been used in stochastic control theory to define measures corresponding to solutions of stochastic DEs with only measurable control laws entering the right-hand sides. The present aim is to show that these same concepts have direct practical application to final value problems with bounded control. This is done here by an example, the noisy integrator: Make E{x21}∣small, subject to dxt = ut dt + dwt, |u|? 1, xt observed. For each control law there is a definite cost v(1?t, x) of starting at x, t and using that law till t = 1, expressible as an integral with respect to (a suitable) P?. By restricting attention to a dense set of smooth laws, using Itô's lemma, Kac's theorem, and the maximum principle for parabolic equations, it is possible to calculate sgn vx for a critical class of control laws, then to compare control laws, “solve” the Bellman-Hamilton-Jacobi equation, and thus justify selection of the obvious bang-bang law as optimal. 相似文献
18.
Milton Rosenberg 《Journal of multivariate analysis》1978,8(2):295-316
Let p, q be arbitrary parameter sets, and let be a Hilbert space. We say that x = (xi)i?q, xi ? , is a bounded operator-forming vector (?Fq) if the Gram matrix 〈x, x〉 = [(xi, xj)]i?q,j?q is the matrix of a bounded (necessarily ≥ 0) operator on , the Hilbert space of square-summable complex-valued functions on q. Let A be p × q, i.e., let A be a linear operator from to . Then exists a linear operator ǎ from (the Banach space) Fq to Fp on (A) = {x:x ? Fq, is p × q bounded on } such that y = ǎx satisfies yj?σ(x) = {space spanned by the xi}, 〈y, x〉 = A〈x, x〉 and . This is a generalization of our earlier [J. Multivariate Anal.4 (1974), 166–209; 6 (1976), 538–571] results for the case of a spectral measure concentrated on one point. We apply these tools to investigate q-variate wide-sense Markov processes. 相似文献
19.
Stanley J Benkoski 《Journal of Number Theory》1976,8(2):218-223
If r, k are positive integers, then denotes the number of k-tuples of positive integers (x1, x2, …, xk) with 1 ≤ xi ≤ n and (x1, x2, …, xk)r = 1. An explicit formula for is derived and it is shown that .If S = {p1, p2, …, pa} is a finite set of primes, then 〈S〉 = {p1a1p2a2…psas; pi ∈ S and ai ≥ 0 for all i} and denotes the number of k-tuples (x1, x3, …, xk) with 1 ≤ xi ≤ n and (x1, x2, …, xk)r ∈ 〈S〉. Asymptotic formulas for are derived and it is shown that . 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