共查询到20条相似文献,搜索用时 15 毫秒
1.
Frames for Fréchet spaces XF with respect to Fréchet sequence spaces ΘF are studied, and conditions implying series expansions in XF and are determined. If is a Θ0-frame for X0 and ΘF (resp. XF) is given, we construct a sequence {Xs}s∈N0, Xs⊂Xs−1, s∈N, (resp. {Θs}s∈N0, Θs⊂Θs−1, s∈N), so that is a pre-F-frame or F-frame for XF with respect to ΘF under different assumptions given on X0, Θ0 and ΘF (resp. XF). 相似文献
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Elke Wolf 《Journal of Mathematical Analysis and Applications》2007,329(1):530-546
We consider weighted Fréchet spaces of holomorphic functions which are defined as countable intersections of weighted Banach spaces of type H∞. We study when these spaces have Stefan Heinrich's density condition and when they are distinguished. 相似文献
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Bivariate Fréchet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, independence and countermonotonicity. They are easily interpretable but have limitations when used as approximations to general dependence structures. To improve the approximation property of the BF copulas and keep the advantage of easy interpretation, we develop a new copula approximation scheme by using BF copulas locally and patching the local pieces together. Error bounds and a probabilistic interpretation of this approximation scheme are developed. The new approximation scheme is compared with several existing copula approximations, including shuffle of min, checkmin, checkerboard and Bernstein approximations and exhibits better performance, especially in characterizing the local dependence. The utility of the new approximation scheme in insurance and finance is illustrated in the computation of the rainbow option prices and stop-loss premiums. 相似文献
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Henrik Petersson 《Journal of Mathematical Analysis and Applications》2006,319(2):764-782
A continuous linear operator is hypercyclic if there is an x∈X such that the orbit {Tnx} is dense, and such a vector x is said to be hypercyclic for T. Recent progress show that it is possible to characterize Banach space operators that have a hypercyclic subspace, i.e., an infinite dimensional closed subspace H⊆X of, except for zero, hypercyclic vectors. The following is known to hold: A Banach space operator T has a hypercyclic subspace if there is a sequence (ni) and an infinite dimensional closed subspace E⊆X such that T is hereditarily hypercyclic for (ni) and Tni→0 pointwise on E. In this note we extend this result to the setting of Fréchet spaces that admit a continuous norm, and study some applications for important function spaces. As an application we also prove that any infinite dimensional separable Fréchet space with a continuous norm admits an operator with a hypercyclic subspace. 相似文献
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For all linear and many nonlinear operators between Fréchet spaces, several continuity results are established. Especially, a new closed graph theorem is given. 相似文献
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Sufficient conditions are found under which the solutions z(t;q) of a semilinear abstract Cauchy problem of the form are Fréchet differentiable with respect to the parameter q. An explicit form is provided for the sensitivity equation satisfied by the Fréchet derivative Dqz(t;q). 相似文献
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Nguyen Huy Chieu 《Journal of Mathematical Analysis and Applications》2008,341(1):247-258
We compute the limiting subdifferential of the indefinite integral of the form where f is an essentially bounded measurable function, or a function continuous on an interval containing (except for, possibly, ), or a step-function which has a countable number of steps around . The related problem of computing the Aumann integral of the limiting subdifferential mapping ∂f(⋅), where f is a Lipschitz real function defined on an open set U⊂Rn, is also investigated. 相似文献
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Krzysztof Piszczek 《Journal of Mathematical Analysis and Applications》2010,361(1):224-233
We characterize quasi-reflexive Fréchet spaces with a basis in terms of the properties of this basis. As a consequence we prove that a Fréchet space with a basis is quasi-reflexive of order one if and only if for every power bounded operator T, either T or T′ is mean ergodic. 相似文献
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Vera Roshchina 《Journal of Mathematical Analysis and Applications》2007,334(1):261-272
In this paper we establish a relationship between the basic subdifferential and upper exhausters of positively homogeneous and polyhedral functions. In the case of a finite exhauster this relationship is represented in a form of an equality, and in the case of a Lipschitz function an inclusion formula is obtained. 相似文献
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Dariusz Bugajewski 《Journal of Mathematical Analysis and Applications》2004,299(2):534-549
In this paper we deal with almost periodic functions with values in a Fréchet space. We apply obtained results to prove the existence of solutions of the initial value problem as well as the Volterra integral equation in this class of functions. We also introduce and investigate asymptotically almost periodic functions with values in a Fréchet space. 相似文献
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Dinh The Luc 《Journal of Mathematical Analysis and Applications》2002,268(2):629-646
We introduce the concept of Fréchet approximate Jacobian matrices for continuous vector functions and use it to establish some sufficient criteria for the local uniqueness of solutions to a variational inequality problem involving continuous, not necessarily locally Lipschitz functions. Examples are also given to illustrate the usefulness of our approach. 相似文献
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I present an inverse function theorem for differentiable maps between Fréchet spaces which contains the classical theorem of Nash and Moser as a particular case. In contrast to the latter, the proof does not rely on the Newton iteration procedure, but on Lebesgue's dominated convergence theorem and Ekeland's variational principle. As a consequence, the assumptions are substantially weakened: the map F to be inverted is not required to be C2, or even C1, or even Fréchet-differentiable. 相似文献
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We study in this paper the first-order behavior of value functions in parametric dynamic programming with linear constraints and nonconvex cost functions. By establishing an abstract result on the Fréchet subdifferential of value functions of parametric mathematical programming problems, some new formulas on the Fréchet subdifferential of value functions in parametric dynamic programming are obtained. 相似文献
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Junhong Ha Shin-ichi Nakagiri Hiroki Tanabe 《Journal of Mathematical Analysis and Applications》2008,346(2):374-383
In this paper we establish the strong Fréchet differentiability of maps from the set of initial values and forcing terms into the set of solutions for semilinear second order evolution equations. Also, under the weaker conditions of nonlinear terms we establish the strong Gâteaux differentiability of the solution maps. An application of results to semilinear strongly damped wave equations is given. 相似文献
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The Mysovskii-type condition is considered in this study for the Secant method in Banach spaces to solve a nonlinear operator equation. We suppose the inverse of divided difference of order one is bounded and the Fréchet derivative of the nonlinear operator is Hölder continuous. By use of Fibonacci generalized sequence, a semilocal convergence theorem is established which matches with the convergence order of the method. Finally, two simple examples are provided to show that our results apply, where earlier ones fail. 相似文献
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The space of all scalarly integrable functions with respect to a Fréchet-space-valued vector measure ν is shown to be a complete Fréchet lattice with the σ-Fatou property which contains the (traditional) space L1(ν), of all ν-integrable functions. Indeed, L1(ν) is the σ-order continuous part of . Every Fréchet lattice with the σ-Fatou property and containing a weak unit in its σ-order continuous part is Fréchet lattice isomorphic to a space of the kind . 相似文献
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Wies?aw ?liwa 《Journal of Mathematical Analysis and Applications》2008,343(2):593-600
Let K be a spherically complete non-archimedean valued field. We prove that the dual space l∞ of the Banach space c0 has a total strongly non-norming subspace M. Using this subspace M we construct a non-normable Fréchet space F of countable type with a continuous norm such that its strong dual is a strict LB-space. Next we show that F has no nuclear Köthe quotient. 相似文献