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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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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.↗
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.↗
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↗
NASA NTRS1977

Characterizations of linear sufficient statistics

A surjective bounded linear operator T from a Banach space X to a Banach space Y must be a sufficient statistic for a dominated family of probability measures defined on the Borel sets of X. These results were applied, so that they characterize linear sufficient statistics for families of the exponential type, including as special cases the Wishart and multivariate normal distributions. The latter result was used to establish precisely which procedures for sampling from a normal population had the property that the sample mean was a sufficient statistic.

Peters, B. C., Jr.↗
NASA NTRS1980

Application of functional analysis to perturbation theory of differential equations

The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

Bogdan, V. M.↗
NASA NTRS1972

Smoothing properties of neutral equations

A neutral functional differential equation is defined as d/dt(Dx sub t) = f(x sub t), with D linear, continuous, atomic at zero. The solution generally is no smoother than the initial data after any finite number of steps. A more restrictive class of D-operators for which some smoothing takes place after an infinite number of steps is defined. This result indicates that a solution can be in an omega-limit set only if it corresponds to initial data which are smooth. A space which can be considered as a Banach space with the topology of uniform convergence is also defined.

Hale, J. K.↗
NASA NTRS1971

Applications of alternative problems

Solution to equations in function space relating linear operator defined in subspace of Banach space and linear or nonlinear operator

Hale, J. K.↗