Now showing items 1-10 of 33
Comparison of smallest eigenvalues and extremal points for third and fourth order three point boundary value problems.
The theory of u₀-positive operators with respect to a cone in a Banach space is applied to the linear differential equations u⁽⁴⁾ + λ₁p(x)u = 0 and u⁽⁴⁾ + λ₂q(x)u = 0, 0 ≤ x ≤ 1, with each satisfying the boundary conditions ...
Glazman-Krein-Naimark theory, left-definite theory, and the square of the Legendre polynomials differential operator.
As an application of a general left-definite spectral theory, Everitt, Littlejohn and Wellman, in 2002, developed the left-definite theory associated with the classical Legendre self-adjoint second-order differential ...
Indecomposability in inverse limits.
Topological inverse limits play an important in the theory of dynamical systems and in continuum theory. In this dissertation, we investigate classical inverse limits of Julia sets and set-valued inverse limits of arbitrary ...
Global SL(2,R) representations of the Schrödinger equation with time-dependent potentials.
We study the representation theory of the solution space of the one-dimensional Schrödinger equation with time-dependent potentials that possess sl₂-symmetry. We give explicit local intertwining maps to multiplier ...
Quadratic Lyapunov theory for dynamic linear switched systems.
In this work, a special class of time-varying linear systems in the arbitrary time scale setting is examined by considering the qualitative properties of their solutions. Building on the work of J. DaCunha and A. Ramos, ...
Existence of positive solutions to right focal three point singular boundary value problems.
In this dissertation, we prove the existence of positive solutions to two classes of three point right focal singular boundary value problems of at least fourth order.
Stable up-downwind finite difference methods for solving Heston stochastic volatility equations.
This dissertation explores effective and efficient computational methodologies for solving two-dimensional Heston stochastic volatility option pricing models with multiple financial engineering applications. Dynamically ...
Moment representations of exceptional orthogonal polynomials.
Exceptional orthogonal polynomials (XOPs) can be viewed as an extension of their classical orthogonal polynomial counterparts. They exclude polynomials of a certain order(s) from being eigenfunctions for their corresponding ...
Boundary conditions associated with left-definite theory and the spectral analysis of iterated rank-one perturbations.
This dissertation details the development of several analytic tools that are used to apply the techniques and concepts of perturbation theory to other areas of analysis. The main application is an efficient characterization ...
The sixth-order Krall differential expression and self-adjoint operators.
We first provide an overview of classical GNK Theory for symmetric, or symmatrizable, differential expressions in L2((a, b);w). Then we review how this theory was applied to find a self-adjoint operator in L2 \mu(-1, 1) ...