Add to ORKGInternational audienceWe consider the problem of finding extremal potentials for the functional determinant of a one-dimensional Schro ̈dinger operator defined on a bounded interval with Dirichlet boundary conditions under an Lq-norm res- triction (q ≥ 1). This is done by first extending the definition of the functional determinant to the case of Lq potentials and showing the resulting problem to be equivalent to a problem in optimal control, which we believe to be of independent interest. We prove existence, uniqueness and describe some basic properties of solutions to this problem for all q ≥ 1, providing a complete characterization of extremal potentials in the case where q is one (a pulse) and two (Weierstrass’s ℘ function)
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We consider the Schr"odinger operator $-Delta+V(x)$ on $H^1_0(Omega)$, where $Omega$ is a given doma...
We derive simple new expressions, in various dimensions, for the functional determinant of a radiall...
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Functional determinants of differential operators play a prominent role in many fields of theoretica...
AbstractWe consider Sturm–Liouville operators on the line segment [0,1] with general regular singula...
Let $M$ be a compact Riemannian manifold with or without boundary, and let $-\Delta $ be its Laplace...
A fundamental result of Solomyak says that the number of negative eigenvalues of a Schrödinger opera...
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