Related papers: de Branges spaces with bi-Lipschitz phase for larg…
The twisted Lie-algebraically deformed relativistic and nonrelativistic phase spaces are constructed with the use of Heisenberg double procedure. The corresponding Heisenberg uncertainty principles are discussed as well.
We develop the concept of pluri-Lagrangian structures for integrable hierarchies. This is a continuous counterpart of the pluri-Lagrangian (or Lagrangian multiform) theory of integrable lattice systems. We derive the multi-time Euler…
We explore the phase space of non-uniform black branes compactified on oblique lattices with a large number of dimensions. We find the phase diagrams for different periodicities and angles, and determine the thermodynamically preferred…
We construct a finite subgroup of Brauer-Manin obstruction for detecting the existence of integral points on integral models of homogeneous spaces of linear algebraic groups of multiplicative type. As application, the strong approximation…
The displacement and deviation vectors in spaces (manifolds), the tangent bundle of which is endowed with a transport along paths, are introduced. In case these spaces are equipped with a linear connection, the deviation equations (between…
In this article, methods from sub-Hardy Hilbert spaces such as the de Branges-Rovnyak spaces and local Dirichlet spaces are used to investigate B\'aez-Duarte's Hilbert space reformulation of the Riemann hypothesis (RH).
In the moduli space of quadratic differentials over complex structures on a surface, we construct a set of full Hausdorff dimension of points with bounded Teichm\"uller geodesic trajectories.The main tool is quantitative nondivergence of…
This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept introduced is the one of a bicomplex…
A characterisation is given of bounded embeddings from weighted $L^2$ spaces on bounded intervals into $L^2$ spaces on the half-plane, induced by isomorphisms given by the Laplace transform onto weighted Hardy and Bergman spaces (Zen…
Intervals in binary or n-ary relations or other discrete structures generalize the concept of interval in a linearly ordered set. Join-irreducible partitions into intervals are characterized in the lattice of all interval decompositions of…
This paper focuses on representations of contractively embedded invariant subspaces in several variables. We present a version of the de Branges theorem for $n$-tuples of multiplication operators by the coordinate functions on analytic…
Let $M$ be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces $H^p$ of differential forms on $M$ and give various characterizations of them, including an atomic decomposition.…
Homogeneous spaces are de Branges' Hilbert spaces of entire functions with the property that certain weighted rescaling transforms induce isometries of the space into itself. A classical example of a homogeneous space is the Paley-Wiener…
A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of…
We extend some results of M.G. Krein to the class of entire functions which can be represented as ratios of discrete Cauchy transforms in the plane. As an application we obtain new versions of de Branges' Ordering Theorem for nearly…
We characterize certain weighted Hardy spaces on the unit disk and completely describe their dual spaces.
We discuss theories in which the standard-model particles are localized on a brane embedded in space-time with large compact extra dimensions, whereas gravity propagates in the bulk. In addition to the ground state corresponding to a…
We study compact polyhedral surfaces as Riemann surfaces and their discrete counterparts obtained through quadrilateral cellular decompositions and a linear discretization of the Cauchy-Riemann equation. By ensuring uniformly bounded…
The moduli spaces for Higgs bundles associated to real Lie groups and a closed Riemann surface have multiple connected components. This survey provides a compendium of results concerning the counting of these components in cases where the…
On any space-like W-surface in the three-dimensional Minkowski space we introduce locally natural principal parameters and prove that such a surface is determined uniquely up to motion by a special invariant function, which satisfies a…