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Articles 1 - 5 of 5
Full-Text Articles in Mathematics
Covariant Representations Of C*-Dynamical Systems Involving Compact Groups, Firuz Kamalov
Covariant Representations Of C*-Dynamical Systems Involving Compact Groups, Firuz Kamalov
Department of Mathematics: Dissertations, Theses, and Student Research
Given a C*-dynamical system (A, G, σ) the crossed product C*-algebra A x σG encodes the action of G on A. By the universal property of A x σG there exists a one to one correspondence between the set all covariant representations of the system (A, G, σ) and the set of all *-representations of A x σG. Therefore, the study of representations of A x σG is equivalent to that of covariant representations of (A, G, σ).
We study induced covariant representations of systems involving compact groups. We prove that every irreducible (resp. factor) covariant …
On Morrey Spaces In The Calculus Of Variations, Kyle Fey
On Morrey Spaces In The Calculus Of Variations, Kyle Fey
Department of Mathematics: Dissertations, Theses, and Student Research
We prove some global Morrey regularity results for almost minimizers of functionals of the form u → ∫Ω f(x, u, ∇u)dx. This regularity is valid up to the boundary, provided the boundary data are sufficiently regular. The main assumption on f is that for each x and u, the function f(x, u, ·) behaves asymptotically like the function h(|·|)α(x), where h is an N-function.
Following this, we provide a characterization of the class of Young measures that can be generated by a sequence …
On A Family Of Generalized Wiener Spaces And Applications, Ian Pierce
On A Family Of Generalized Wiener Spaces And Applications, Ian Pierce
Department of Mathematics: Dissertations, Theses, and Student Research
We investigate the structure and properties of a variety of generalized Wiener spaces. Our main focus is on Wiener-type measures on spaces of continuous functions; our generalizations include an extension to multiple parameters, and a method of adjusting the distribution and covariance structure of the measure on the underlying function space.
In the second chapter, we consider single-parameter function spaces and extend a fundamental integration formula of Paley, Wiener, and Zygmund for an important class of functionals on this space. In the third chapter, we discuss measures on very general function spaces and introduce the specific example of a generalized …
The Theory Of Discrete Fractional Calculus: Development And Application, Michael T. Holm
The Theory Of Discrete Fractional Calculus: Development And Application, Michael T. Holm
Department of Mathematics: Dissertations, Theses, and Student Research
The author's purpose in this dissertation is to introduce, develop and apply the tools of discrete fractional calculus to the arena of fractional difference equations. To this end, we develop the Fractional Composition Rules and the Fractional Laplace Transform Method to solve a linear, fractional initial value problem in Chapters 2 and 3. We then apply fixed point strategies of Krasnosel'skii and Banach to study a nonlinear, fractional boundary value problem in Chapter 4.
Adviser: Lynn Erbe and Allan Peterson
Formalizing Categorical And Algebraic Constructions In Operator Theory, William Benjamin Grilliette
Formalizing Categorical And Algebraic Constructions In Operator Theory, William Benjamin Grilliette
Department of Mathematics: Dissertations, Theses, and Student Research
In this work, I offer an alternative presentation theory for C*-algebras with applicability to various other normed structures. Specifically, the set of generators is equipped with a nonnegative-valued function which ensures existence of a C*-algebra for the presentation. This modification allows clear definitions of a "relation" for generators of a C*-algebra and utilization of classical algebraic tools, such as Tietze transformations.