On a theorem of Hochstadt

Borg-type Theorems for Generalized Jacobi Matrices and Trace Formulas

The paper deals with two types of inverse spectral problems for the class of generalized Jacobi matrices introduced in [9]. Following the scheme proposed in [5], we deduce analogs of the Hochstadt–Lieberman theorem and the Borg theorem. Properties of a Weyl function of the generalized Jacobi matrix are systematically used to prove the uniqueness theorems. Trace formulas for the generalized Jaco...

Abstract Reduction Semantics for Modular Higher-Order Contract Verification

Reduction Semantics for Modular Higher-Order Contract Verification Sam Tobin-Hochstadt David Van Horn

Modern Algebra with Applications

On Tychonoff's type theorem via grills

‎Let ${X_{alpha}:alphainLambda}$ be a collection of topological spaces‎, ‎and $mathcal {G}_{alpha}$ be a grill on $X_{alpha}$ for each $alphainLambda$‎. ‎We consider Tychonoffrq{}s type Theorem for $X=prod_{alphainLambda}X_{alpha}$ via the above grills and a natural grill on $X$ ‎related to these grills, and present a simple proof to this theorem‎. ‎This immediately yields the classical theorem...

Eigenvalue Asymptotics of Layered Media and Their Applications to the Inverse Problem

We compute the asymptotics of the eigenvalues of the classical Sturm–Liouville problem with a piecewise smooth coefficient q. This means that q and/or its derivatives can have jump discontinuities. The boundary conditions are arbitrary. Our results extend the classical work of H. Hochstadt (see [Comm. Pure Appl. Math., 14 (1961), pp. 749–764]) and some related formulas discovered by G. Borg (se...