Related papers: Duality of capacities and Sobolev extendability in…

The concept of electric-magnetic duality can be extended to linearized gravity. It has indeed been established that in four dimensions, the Pauli-Fierz action (quadratic part of the Einstein-Hilbert action) can be cast in a form that is…

A global analysis of duality transformations is presented. It is shown that duality between quantum field theories exists only when the geometrical structure of the quantum configuration spaces of the theories comply with certain precise…

An $L^2$ version of the Serre duality on domains in complex manifolds involving duality of Hilbert space realizations of the $\bar{\partial}$-operator is established. This duality is used to study the solution of the…

We show that Sobolev space $W^1_1(\Omega)$ of any planar one-connected domain $\Omega$ has the Bounded Approximation property. The result holds independently from the properties of the boundary of $\Omega$. The prove is based on a new…

By using some elementary techniques from operator theory, we prove constructively prove the existence of solutions to Dirichl\'et problems for planar Jordan domains with at least two boundary curves. An iterative method is thus obtained,…

We study several quantities associated to the Green's function of a multiply connected domain in the complex plane. Among them are some intrinsic properties such as geodesics, curvature, and $L^2$-cohomology of the capacity metric and…

We consider the problem of two capacitively coupled Josephson junction arrays made of ultrasmall junctions. Each one of the arrays can be in the semiclassical or quantum regimes, depending on their physical parameter values. The former case…

In this short note we show an equivalence between Sobolev type inequalities and so called isocapacitary inequalities in the context of a large class of nonlinear Dirichlet forms, their associated Dirichlet spaces and their associated…

Generalizing Courant's nodal domain theorem, the "Extended Courant property" is the statement that a linear combination of the first $n$ eigenfunctions has at most $n$ nodal domains. In a previous paper (Documenta Mathematica, 2018, Vol.…

Imposing an extensional uniformity condition on a non-uniform circuit complexity class C means simply intersecting C with a uniform class L. By contrast, the usual intensional uniformity conditions require that a resource-bounded machine be…

I explore several related routes to deriving the Jordan-algebraic structure of finite-dimensional quantum theory from more transparent operational or physical principles, mainly involving ideas about the symmetries of, and the correlations…

We show that $W^{1,1}(\mathbb{R}^2)$ has the Daugavet property when endowed with the norm induced by the $L^1$-norm of the gradient, but fails to have the slice diameter two property when equipped with the usual Sobolev norm.

According to Courant's theorem, an eigenfunction as\-sociated with the $n$-th eigenvalue $\lambda\_n$ has at most $n$ nodal domains. A footnote in the book of Courant and Hilbert, states that the same assertion is true for any linear…

A Fenchel-Moreau type duality for proper convex and lower semi-continuous functions $f\colon X\to \overline{L^0}$ is established where $(X,Y,\langle \cdot,\cdot \rangle)$ is a dual pair of Banach spaces and $\overline{L^0}$ is the set of…

Let X and Y be planar Jordan domains of the same finite connectivity, Y being inner chordarc regular (such are Lipschitz domains). Every homeomorphism h:X->Y in the Sobolev space $W^{1,2}$ extends to a continuous map between closed domains.…

Montonen-Olive duality implies that the categories of A-branes on the moduli spaces of Higgs bundles on a Riemann surface C for a pair of Langlands-dual groups are equivalent. We reformulate this as a statement about categories of B-branes…

Using a generalization of complexes, called 2-complexes, this paper defines and analyzes new Sobolev spaces of matrix fields and their interrelationships within a commuting diagram. These spaces have very weak second-order derivatives. An…

Among the many important geometric properties of quantum state space are: transitivity of the group of symmetries of the cone of unnormalized states on its interior (homogeneity), identification of this cone with its dual cone of effects…

In this paper we study when the Kobayashi distance on a Kobayashi hyperbolic domain has certain visibility properties, with a focus on unbounded domains. "Visibility" in this context is reminiscent of visibility, seen in negatively curved…

We give explicit necessary and sufficient conditions for the boundedness of the general second order differential operator L with real- or complex-valued distributional coefficients acting from the Sobolev space W^{1,2}(R^n) to its dual…