Allan M. Krall

Modeling stabilization and control of serially connected beams

Many flexible structures consist of a large number of components coupled end to end in the form of a chain. In this paper, we consider the simplest type of such structures which is formed by N seri...

Orthogonal Polynomials Satisfying Fourth Order Differential Equations

Since they are rather important and quite accessible, we repeat the general theoretical facts concerning weights, moments and polynomials pertaining to fourth order differential equations. We then briefly discuss the squares of the differential equations of the second order, giving a number of easily derived examples of fourth order problems. This is followed by three new orthogonal polynomial sets satisfying fourth order differential equations, but which do not satisfy second order differential equations.

M (λ) theory for singular Hamiltonian systems with two singular points

The theory of singular Hamiltonian systems is developed. Square integrable solutions are exhibited and used to define Green’s function. Using a singular Green’s formula, other self-adjoint boundary value problems are generated in which regular and singular boundary conditions are mixed together. Finally the spectral measure, the generalized Fourier transform of an arbitrary function, and the inverse transform for problems with separated boundary conditions are derived.

Distributional Weight Functions for Orthogonal Polynomials

Given any collection of real numbers

Spectral Analysis of Non‐Selfadjoint Discrete Schrödinger Operators with Spectral Singularities

\{ \mu _i \} _{i = 0}^\infty

Orthogonal polynomials and higher order singular Sturm-Liouville systems

, called moments, satisfying a Hamburger-like condition

Boundary values for an eigenvalue problem with a singular potential

\Delta _n = \det [\mu _{i + j} ]_{i,j = 0}^n \ne 0

Orthogonal Polynomials through Moment Generating Functionals

and a growth condition

Asymptotic stability of the Euler-Bernoulli beam with boundary control

| {\mu _n } | < cM^n n!

Laguerre polynomial expansions in indefinite inner product spaces

, where c, M are constant,