Showing papers by "Don B. Hinton published in 1984"
TL;DR: In this article, the boundary conditions for differential systems in intermediate limit situations were discussed, including the n -th order, scalar, limit-n case, as well as the n dimensional limit- n, first order case.
Abstract: Publisher Summary This chapter discusses the boundary conditions for differential systems in intermediate limit situations. One of the major obstacles in the development of the singular Sturm–Liouville theory for n dimensional vector systems is the appropriate definition and proof of the existence of boundary conditions. The chapter presents such a development. It includes the n -th order, scalar, limit- n case, as well as the n dimensional limit- n , first order case. The chapter considers the n dimensional vector system.
5 citations
TL;DR: In this article, asymptotic solutions for disconjugate differential equations are derived for a class of differential equations which are disconjoint and the method of proof requires a variation of the classical Levinson theorem.
Abstract: Asymptotic solutions are derived for a class of differential equations which are disconjugate. The method of proof requires a variation of the classical Levinson theorem. Applications to spectral theory are given.
1 citations
TL;DR: In this paper, the authors considered the asymptotic form of the Titchmarsh-Weyl coefficient for the fourth order equation y (4) + q(x)y = λ y, where q (x) is real and locally integrable.
Abstract: This paper considers the asymptotic form, as λ tends to infinity in sectors omitting the real axis, of the matrix Titchmarsh-Weyl coefficient M (λ) for the fourth order equation y (4) + q(x)y = λ y , where q(x) is real and locally absolutely integrable. By letting M 0 (λ) denote the m -coefficient for the Fourier case y (4) = λ y , the asymptotic formula M (λ) = M 0 (λ) + 0(1) is established.
1 citations
TL;DR: In this paper, the pole structure of the Titchmarsh-Weyl m-coefficients is connected with the spectrum of a Hamiltonian system which is singular at each end of an interval.
Abstract: In this paper we connect the pole structure of the Titchmarsh-Weyl m-coefficients with the spectrum of a Hamiltonian system which is singular at each end of an interval. Characterizations are given for the resolvent set, point spectrum, continuous spectrum and point-continuous spectrum. We allow the system to be of either limit point or limit circle type at each end.