共查询到20条相似文献,搜索用时 0 毫秒
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A. G. Azpeitia 《International Journal of Mathematical Education in Science & Technology》2013,44(5):813-817
The distance from a point to a linear variety defined by a finite intersection of hyperplanes is equal to the maximum of the distances from the point to all the hyperplanes which contain the variety. 相似文献
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Jaroslav Tiser 《Transactions of the American Mathematical Society》2003,355(8):3277-3289
It is shown that the statement of the Vitali Covering Theorem does not hold for a certain class of measures in a Hilbert space. This class contains all infinite-dimensional Gaussian measures.
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William C. Lyford 《Mathematische Annalen》1975,217(3):257-261
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Thomas Lorenz 《Journal of Mathematical Analysis and Applications》2018,457(2):1502-1567
Applications in robust control problems and shape evolution motivate the mathematical interest in control problems whose states are compact (possibly non-convex) sets rather than vectors. This leads to evolutions in a basic set which can be supplied with a metric (like the well-established Pompeiu–Hausdorff distance), but it does not have an obvious linear structure. This article extends differential inclusions with state constraints to compact-valued states in a separable Hilbert space H. The focus is on sufficient conditions such that a given constraint set (of compact subsets) is viable a.k.a. weakly invariant. Our main result extends the tangential criterion in the well-known viability theorem (usually for differential inclusions in a vector space) to the metric space of non-empty compact subsets of H. 相似文献
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I. P. Ryazantseva 《Russian Mathematics (Iz VUZ)》2016,60(11):45-57
In a Hilbert space we construct a regularized continuous analog of the Newton method for nonlinear equation with a Fréchet differentiable and monotone operator. We obtain sufficient conditions of its strong convergence to the normal solution of the given equation under approximate assignment of the operator and the right-hand of the equation. 相似文献
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Stephane Jaffard Robert M. Young 《Proceedings of the American Mathematical Society》1998,126(2):553-560
A sequence of vectors in a separable Hilbert space is said to be a Schauder basis for if every element has a unique norm-convergent expansion
If, in addition, there exist positive constants and such that
then we call a Riesz basis. In the first half of this paper, we show that every Schauder basis for can be obtained from an orthonormal basis by means of a (possibly unbounded) one-to-one positive self adjoint operator. In the second half, we use this result to extend and clarify a remarkable theorem due to Duffin and Eachus characterizing the class of Riesz bases in Hilbert space.
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Nguyen Buong 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(12):4534-2466
The purpose of this paper is to prove the strong convergence of a method combining the descent method and the hybrid method in mathematical programming for finding a point in the common fixed point set of a semigroup of nonexpansive mappings in Hilbert space. 相似文献
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Jorge A. León 《Applied Mathematics and Optimization》1993,27(3):313-327
Let (X,l,) be a measure space, letW be a cylindrical Hilbert-Wiener process, and let be an anticipating integrable process-valued function onX. We prove, under natural assumptions on, that there exists a measurable version Yx,x X, of the anticipating integral of(x) such that the integral x Yx(dx) is a version of the anticipating integral of X
(x)(dx). We apply this anticipating Fubini theorem to study solutions of a class of stochastic evolution equations in Hilbert space. 相似文献
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Gerd Rodé 《Journal of Mathematical Analysis and Applications》1982,85(1):172-178
J. B. Baillon [C. R. Acad. Sci. Paris Ser. A.280 (1975), 1511–1514] proved an ergodic theorem for a single nonexpansive mapping in a Hilbert space, which is a nonlinear version of von Neumann's mean ergodic theorem. In this paper, we study the ergodic behavior of a semigroup of nonexpansive mappings. We try to find a sequence of means on the semigroup, generalizing the Cesàro means on , such that the corresponding sequence of nonexpansive mappings converges to a projection onto the set of common fixed-points. Our method of proof is an appropriate modification of A. Pazy's proof [Israel J. Math.26 (1977), 197–204] of Baillon's theorem. 相似文献
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A general parametric nonlinear mathematical programming problem with an operator equality constraint and a finite number of functional inequality constraints is considered in a Hilbert space. Elements of a minimizing sequence for this problem are formally constructed from elements of minimizing sequences for its augmented Lagrangian with values of dual variables chosen by applying the Tikhonov stabilization method in the course of solving the corresponding modified dual problem. A sequential Kuhn-Tucker theorem in nondifferential form is proved in terms of minimizing sequences and augmented Lagrangians. The theorem is stable with respect to errors in the initial data and provides a necessary and sufficient condition on the elements of a minimizing sequence. It is shown that the structure of the augmented Lagrangian is a direct consequence of the generalized differentiability properties of the value function in the problem. The proof is based on a “nonlinear” version of the dual regularization method, which is substantiated in this paper. An example is given illustrating that the formal construction of a minimizing sequence is unstable without regularizing the solution of the modified dual problem. 相似文献
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A. N. Godunov 《Mathematical Notes》1974,15(3):273-279
We formulate a continuous function FR×HH, where H is a separable Hilbert space such that the Cauchy problem. x(t)=F(t, x(t)), x(t0)=x0 has no solution in any neighborhood of the point t0, no matter what t0 R and x0 H are considered.Translated from Matematicheskie Zametki, Vol. 15, No. 3, pp. 467–477, March, 1974.In conclusion, the author thanks O. G. Smolyanov and V. I. Averbukh for their constant interest and for a number of useful remarks. 相似文献
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J. Feldman 《Israel Journal of Mathematics》1965,3(2):99-103
A short proof of the Levy continuity theorem in Hilbert space.
In the theory of the normal distribution on a real Hilbert spaceH, certain functionsφ have been shown by L. Gross to give rise to random variablesφ∼ in a natural way; in particular, this is the case for functions which are “uniformly τ-continuous near zero”. Among such
functions are the characteristic functionsφ of probability distributionsm onH, given byφ(y)=∫e
i(y,x)dm(x). The following analogue of the Levy continuity theorem has been proved by Gross: Letφ
j be the characteristic function of the probability measurem
j onH, Then necessary and sufficient that ∫f dm
j → ∫f dm for some probability measurem and all bounded continuousf, is that there exists a functionφ, uniformly τ-continuous near zero, withφ
j∼ →φ∼ in probability.φ turns out, of course, to be the characteristic function ofm. In the present paper we give a short proof of this theorem.
Research supported by National Science Foundation Grant GP-3977. 相似文献
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Let H be a Hilbert space with inner product (⋅,⋅) and ‖⋅‖ norm, and let K be weakly compact a subset of H. Let be nonlinear mapping and be a nonlinear bounded mapping. In this paper, we define the I-asymptotically quasi-nonexpansive mapping in Hilbert space. If T is an I-asymptotically quasi-nonexpansive mapping, then we prove that , for u∈K as n→∞, is weakly almost convergent to its asymptotic center. 相似文献