69 citations · 166 across the 9 of their papers we have counts for
10 papers
Fourth order Saint-Venant inequalities: maximizing compliance and mean deflection among clamped plates
Mark Ashbaugh, Dorin Bucur, Richard S. Laugesen +1
We prove a fourth order analogue of the Saint-Venant inequality: the mean deflection of a clamped plate under uniform transverse load is maximal for the ball, among plates of presc…
Spectral gaps of 1-D Robin Schrödinger operators with single-well potentials
Mark S. Ashbaugh, Derek Kielty
We prove sharp lower bounds on the spectral gap of 1-dimensional Schrödinger operators with Robin boundary conditions for each value of the Robin parameter. In particular, our lowe…
Trace formulas applied to the Riemann -function
Mark S. Ashbaugh, Fritz Gesztesy, Lotfi Hermi +3
We use a spectral theory perspective to reconsider properties of the Riemann zeta function. In particular, new integral representations are derived and used to present its value at…
A bound for the eigenvalue counting function for Krein--von Neumann and Friedrichs extensions
Mark S. Ashbaugh, Fritz Gesztesy, Ari Laptev +2
For an arbitrary open, nonempty, bounded set , , and sufficiently smooth coefficients , we consider the closed, strictly positive, h…
A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains
Mark S. Ashbaugh, Fritz Gesztesy, Marius Mitrea +2
In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of…
Spectral Theory for Perturbed Krein Laplacians in Nonsmooth Domains
Mark S. Ashbaugh, Fritz Gesztesy, Marius Mitrea +1
We study spectral properties for , the Krein--von Neumann extension of the perturbed Laplacian defined on , where is measurable, bounded and nonn…