Optimal domains for kernel operators on [0,∞)×[0,∞)

On Kernel Representation of Linear Operators

A note on the heat kernel coefficients for nonminimal operators

We consider certain results for the heat kernel of nonminimal operators. The general expressions provided by Gusynin and Kornyak resulting from symbolic computation programmes for n dimensions are evaluated for 4 dimensions which are checked against results given by Barvinsky and Vilkovisky. We also check that the results in flat space are consistent with earlier results of Guendelmen et al. We...

Narrowing Operators on Template Abstract Domains

In the theory of abstract interpretation, narrowing operators are used to improve the precision of the analysis after a post-fixpoint has been reached. This is especially true on numerical domains, since they are generally endowed with infinite descending chains which may lead to a non-terminating analysis in the absence of narrowing. We provide an abstract semantics which improves the analysis...

Optimal Transport on Discrete Domains

Many tools from discrete differential geometry (DDG) were inspired by practical considerations in areas like computer graphics and vision. Disciplines like these require fine-grained understanding of geometric structure and the relationships between different shapes—problems for which the toolbox from smooth geometry can provide substantial insight. Indeed, a triumph of discrete differential ge...

Composition operators between growth spaces‎ ‎on circular and strictly convex domains in complex Banach spaces‎

‎Let $\Omega_X$ be a bounded‎, ‎circular and strictly convex domain in a complex Banach space $X$‎, ‎and $\mathcal{H}(\Omega_X)$ be the space of all holomorphic functions from $\Omega_X$ to $\mathbb{C}$‎. ‎The growth space $\mathcal{A}^\nu(\Omega_X)$ consists of all $f\in\mathcal{H}(\Omega_X)$‎ ‎such that $$|f(x)|\leqslant C \nu(r_{\Omega_X}(x)),\quad x\in \Omega_X,$$‎ ‎for some constant $C>0$‎...