Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 70-73). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 70-73). Also available on the Internet.

Thesis (M.S.)--Florida State University, 2004. / Advisor: Dr. Xiuwen Liu, Florida State University, College of Arts and Sciences, Dept. of Computer Science. Title and description from dissertation home page (viewed June 17, 2004). Includes bibliographical references.

The theory of semigroups of linear operators forms an integral part of Functional Analysis with substantial applications to many fields of the natural sciences. In this study we are concerned with the application to equations of mathematical physics. The theory of semigroups of bounded linear operators is closely related to the solvability of evolution equations in Banach spaces that model time dependent processes in nature. Well-posed evolution problems give rise to a semigroup of bounded linear operators. However, in many important and interesting cases the problem is ill-posed making it inaccessible to the classical semigroup theory. One way of dealing with this problem is to generalize the theory of semigroups. In this thesis we give an outline of the theory of two such generalizations, namely, C-regularized semigroups and B-bounded semigroups, with the inter-relations between them and show a number of applications to ill-posed problems. / Thesis (Ph.D.)-University of Natal, Durban, 2001.

Thesis (Ph. D.)--Stanford University, 1987. / "June 1987." "Also numbered Classic-87-03"--Cover. "This research was supported by NASA Ames Consortium Agreement NASA NCA2-150 and Office of Naval Research Contracts N00014-86-K-0565, N00014-82-K-0335, N00014-75-C-1132"--P. vi. Includes bibliographical references (p. 125-129).

<p> In this thesis we study convexity theorems on the interpolation of linear operators between LP-spaces. An extension of the Riesz-Thorin Theorem to spaces constructed from countably many LP-spaces is given. In addition, results involving analytic families of linear operators between these spaces are obtained. </p> / Thesis / Master of Science (MSc)

Thesis (MSc)--Stellenbosch University, 2013. / Please refer to full text to view abstract.

In this thesis we study Floquet theory on a Banach space. We are concerned about the linear differential equation of the form: y'(t) = A(t)y(t), where t ∈ R, y(t) is a function with values in a Banach space X, and A(t) are linear, bounded operators on X. If the system is periodic, meaning A(t+ω) = A(t) for some period ω, then it is called a Floquet system. We will investigate the existence and uniqueness of the periodic solution, as well as the stability of a Floquet system. This thesis will be presented in five main chapters. In the first chapter, we review the system of linear differential equations on Rn: y'= A(t)y(t) + f(t), where A(t) is an n x n matrix-valued function, y(t) are vectors and f(t) are functions with values in Rn. We establish the general form of the all solutions by using the fundamental matrix, consisting of n independent solutions. Also, we can find the stability of solutions directly by using the eigenvalues of A. In the second chapter, we study the Floquet system on Rn, where A(t+ω) = A(t). We establish the Floquet theorem, in which we show that the Floquet system is closely related to a linear system with constant coefficients, so the properties of those systems can be applied. In particular, we can answer the questions about the stability of the Floquet system. Then we generalize the Floquet theory to a linear system on Banach spaces. So we introduce to the readers Banach spaces in chapter three and the linear operators on Banach spaces in chapter four. In the fifth chapter we study the asymptotic properties of solutions of the system: y'(t) = A(t)y(t), where y(t) is a function with values in a Banach space X and A(t) are linear, bounded operators on X with A (t+ω) = A(t). For that system, we can show the evolution family U(t,s) representing the solutions is periodic, i.e. U(t+ω, s+ω) = U(t,s). Next we study the monodromy of the system V := U(ω,0). We point out that the spectrum set of V actually determines the stability of the Floquet system. Moreover, we show that the existence and uniqueness of the periodic solution of the nonhomogeneous equation in a Floquet system is equivalent to the fact that 1 belongs to the resolvent set of V.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 136-138). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 136-138). Also available on the Internet.