Second Order Sturm Liouville Difference Equations And Orthogonal Polynomials
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Second-Order Sturm-Liouville Difference Equations and Orthogonal Polynomials
This memoir presents machinery for analyzing many discrete physical situations, and should be of interest to physicists, engineers, and mathematicians. We develop a theory for regular and singular Sturm-Liouville boundary value problems for difference equations, generalizing many of the known results for differential equations. We discuss the self-adjointness of these problems as well as their abstract spectral resolution in the appropriate [italic capital]L2 setting, and give necessary and sufficient conditions for a second-order difference operator to be self-adjoint and have orthogonal polynomials as eigenfunctions.
Integrable Systems and Riemann Surfaces of Infinite Genus
Author: Martin Ulrich Schmidt
language: en
Publisher: American Mathematical Soc.
Release Date: 1996
This memoir develops the spectral theory of the Lax operators of nonlinear Schrödinger-like partial differential equations with periodic boundary conditions. Their special curves, i.e., the common spectrum with the periodic shifts, are generically Riemann surfaces of infinite genus. The points corresponding to infinite energy are added. The resulting spaces are no longer Riemann surfaces in the usual sense, but they are quite similar to compact Riemann surfaces.
Pseudofunctors on Modules with Zero Dimensional Support
Author: I-Chiau Huang
language: en
Publisher: American Mathematical Soc.
Release Date: 1995
Pseudofunctors with values on modules with zero dimensional support are constructed over the formally smooth category and residually finite category. Combining those pseudofunctors, a pseudofunctor over the category whose objects are Noetherian local rings and whose morphisms are local with finitely generated residue field extensions is constructed.