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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Spectral dilation of L(B,H)-valued measures and its application to stationary dilation for Banach space valued processes

Let B be a Banach space and H and K two Hilbert spaces. The spectral dilation of L(B,H)-valued measures is studied and it is shown that the recent results of Makagon and Salehi (1986) and Rosenberg (1982) on the dilation of L(K,H)-valued measures can be extended to hold for the general Banach space setting of L(B,H)-valued measures. These L(B,H)-valued measures are closely connected to the Banach space valued processes. This connection is recalled and as application of spectral dilation of L(B,H)-valued measures the well known stationary dilation results for scalar valued processes is extended to the case of Banach space valued processes.

Miamee, A. G.↗
NASA NTRS1989

Spectral dilation of L(B,H)-valued measures and its application to stationary dilation for Banach space valued processes

Let B be a Banach space and H and K to Hilbert spaces. The spectral dilation of L(B,H)-valued measures is studied and it is shown that the recent results of Makagon and Salehi (1986) and Rosenberg (1982) on the dilation of L(K,H)-valued measures can be extended to hold for the general Banach space setting of L(B,H)-valued measures. These L(B,H)-valued measures are closely connected to the Banach space valued processes. This connection is recalled and as application of spectral dilation of L(B,H)-valued measures the well known stationary dilation results for scalar valued processes is extended to the case of Banach space valued processes.

Miamee, A. G.↗
DOE OSTI2018

Fundamental Operator-Valued Functions of Singular Integrodifferential Operators in Banach Spaces

In this paper, using methods of the theory of generalized functions in Banach spaces, we examine the Cauchy problem for an abstract integrodifferential equation of a specific type. Under the assumption that there exist the complete Jordan structure of the differential part of the equation and the order of the zero of the kernel of the integral part, the fundamental operator-valued function (the fundamental solution) is constructed for the corresponding integrodifferential operator, which is used for further investigation of the problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On Stability of Perturbed Semigroups in Partially Ordered Banach Spaces

We prove necessary and sufficient stability conditions for perturbed semigroups of linear operators in Banach spaces with cones and consider examples using these conditions. In particular, we consider an example where the boundary-value problem is perturbed by a linear operator with a delayed independent variable and establish stability conditions for such a perturbed semigroup.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

The Quest for the Ultimate Anisotropic Banach Space

We present a new scale U{sub p}{sup t,s} (s<−t<0 and 1≤p<∞) of anisotropic Banach spaces, defined via Paley–Littlewood, on which the transfer operator L{sub g}φ=(g⋅φ)∘T{sup −1} associated to a hyperbolic dynamical system T has good spectral properties. When p=1 and t is an integer, the spaces are analogous to the “geometric” spaces B{sup t,|s+t|} considered by Gouëzel and Liverani (Ergod Theory Dyn Syst 26:189–217, 2006). When p>1 and −1+1/p<s<−t<0<t<1/p, the spaces are somewhat analogous to the geometric spaces considered by Demers and Liverani (Trans Am Math Soc 360:4777–4814, 2008). In addition, just like for the “microlocal” spaces defined by Baladi and Tsujii (Ann Inst Fourier 57:127–154, 2007) (or Faure–Roy–Sjöstrand in Open Math J 1:35–81, 2008), the transfer operator acting on U{sub p}{sup t,s} can be decomposed into L{sub g,b}+L{sub g,c}, where L{sub g,b} has a controlled norm while a suitable power of L{sub g,c} is nuclear. This “nuclear power decomposition” enhances the Lasota–Yorke bounds and makes the spaces U{sub p}{sup t,s} amenable to the kneading approach of Milnor–Thurson (Dynamical Systems (Maryland 1986–1987), Springer, Berlin, 1988) (as revisited by Baladi–Ruelle, Baladi in Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps, Monograph, 2016; Baladi and Ruelle in Ergod Theory Dyn Syst 14:621–632, 1994; Baladi and Ruelle in Invent Math 123:553–574, 1996) to study dynamical determinants and zeta functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1976

Stability of interconnected dynamical systems described on Banach spaces

New stability results for a large class of interconnected dynamical systems (also called composite systems or large scale systems) described on Banach spaces are established. In the present approach, the objective is always the same: to analyze large scale systems in terms of their lower order and simpler subsystems and in terms of their interconnecting structure. The present results provide a systematic procedure of analyzing hybrid dynamical systems (i.e., systems that are described by a mixture of different types of equations). To demonstrate the method of analysis advanced, two specific examples are considered.

Rasmussen, R. D.↗
DOE OSTI2016

Extrapolation of operators acting into quasi-Banach spaces

Linear and sublinear operators acting from the scale of L{sub p} spaces to a certain fixed quasinormed space are considered. It is shown how the extrapolation construction proposed by Jawerth and Milman at the end of 1980s can be used to extend a bounded action of an operator from the L{sub p} scale to wider spaces. Theorems are proved which generalize Yano's extrapolation theorem to the case of a quasinormed target space. More precise results are obtained under additional conditions on the quasinorm. Bibliography: 35 titles.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1962

Periodic Motions in Banach Space and Applications to Functional-Differential Equations

In establishing the existence of periodic solutions for nonautonomous differential equations of the form x = g(x, t), where g is periodic in t of period ω for fixed x, it is often convenient to consider the translation operator T(x(t)) = x(t + ω). If corresponding to each initial vector chosen in an appropriate region there corresponds a unique solution of our equation, then periodicity may be established by proving the existence of a fixed point under T. This same technique is also useful for more general functional equations and can be extended in a number of interesting ways. In this paper we shall consider a variable type of translation operator which is useful in investigating periodicity for autonomous differential and functional equations where the period involved is less obvious.

Jones, G. Stephen↗
DOE OSTI2018

Analytic in a Sector Resolving Families of Operators for Degenerate Evolution Fractional Equations

We introduce a class of pairs of operators defining a linear homogeneous degenerate evolution fractional differential equation in a Banach space. Reflexive Banach spaces are represented as the direct sums of the phase space of the equation and the kernel of the operator at the fractional derivative. In a sector of the complex plane containing the positive half-axis, we construct an analytic family of resolving operators that degenerate only on the kernel. The results are used in the study of the solvability of initial-boundary value problems for partial differential equations containing fractional time-derivatives and polynomials in the Laplace operator with respect to the spatial variable.

97 MATHEMATICS AND COMPUTING↗