Topic #7 --------------- OP-SF NET --------------- February 9, 1995 ~~~~~~~~~ From: Notices Amer. Math. Soc., January 1995 Subject: New Memoir on Spectral Theory and Orthogonal Polynomials The following AMS Memoir appeared: A. Jirari, "Second-order Sturm-Liouville equations and orthogonal polynomials", Memoirs AMS, Vol. 113, Number 542, 1995. From the abstract: The book develops a theory for regular and singular Sturm-Liouville boundary problems for difference equations, generalizing many of the known results for differential equations. Discussing the self-adjointness of these problems as well as their abstract spectral resolution in the appropriate $L^2$ setting. the book gives necessary and sufficient conditions for a second-order difference operator to be self-adjoint and have orthogonal polynomials as eigenfunctions.