Related papers: A representing system generated by the Szeg\"{o} k…
This paper presents a new way of describing cross fields based on fourth order tensors. We prove that the new formulation is forming a linear space in $\mathbb{R}^9$. The algebraic structure of the tensors and their projections on…
We compute the Szeg\"o kernels of the unit circle bundles of homogeneous negative line bundles over a compact Hermitian symmetric space. We prove that their logarithmic terms vanish in all cases and, further, that the circle bundles are not…
Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group $SL(2,C)\otimes SL(2,C)$, composed of local operators acting on the binary…
In this paper, we are mainly concerned with the well-posed problem of the fractional Keller--Segel system in the framework of variable Lebesgue spaces. Based on carefully examining the algebraical structure of the system, we reduced the…
Let $M$ be complex projective manifold, and $A$ a positive line bundle on it. Assume that $SU(2)$ acts on $M$ in a Hamiltonian manner, with nowhere vanishing moment map, and that this action linearizes to $A$. Then there is an associated…
We continue the study of the following Hamiltonian equation on the Hardy space of the circle, $$i\partial _tu=\Pi(|u|^2u)\ ,$$ where $\Pi $ denotes the Szeg\"o projector. This equation can be seen as a toy model for totally non dispersive…
We present a proof of Kemer's representability theorem for affine PI algebras over a field of characteristic zero.
We prove a variant of the multidimensional polynomial Szemer\'edi theorem of Bergelson and Leibman where one replaces polynomial sequences with other sparse sequences defined by functions that belong to some Hardy field and satisfy certain…
We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…
Products of Siegel upper half spaces are Siegel domains, whose Silov boundaries have the structure of products $\mathscr H_1\times\mathscr H_2$ of Heisenberg groups. By the reproducing formula of bi-parameter heat kernel associated to…
Using the structure of the Boson-Fermion Fock space and an argument taken from [2], we give a new proof of the triviality of the $L^2$ cohomology groups on an abstract Wiener space, alternative to that given by Shigekawa [9]. We apply some…
Special orthogonal matrices with rational elements form the group SO(n,Q), where Q is the field of rational numbers. A theorem describing the structure of an arbitrary matrix from this group is proved. This theorem yields an algorithm for…
In a previous work the authors gave a conceptual explanation for the linearity of the Weil representation over a finite field k of odd characteristic: There exists a canonical system of intertwining operators between the Lagrangian models…
We interpret certain equivariant Kasparov groups as equivariant representable K-theory groups. We compute these groups via a classifying space and as K-theory groups of suitable sigma-C*-algebras. We also relate equivariant vector bundles…
Square COD (complex orthogonal design) with size $[n, n, k]$ is an $n \times n$ matrix $\mathcal{O}_z$, where each entry is a complex linear combination of $z_i$ and their conjugations $z_i^*$, $i=1,\ldots, k$, such that $\mathcal{O}_z^H…
A set of reproducing kernel Hilbert spaces are obtained on Hilbert spaces over quaternion slices with the aid of coherent states. It is proved that the so obtained set forms a measurable field of Hilbert spaces and their direct integral…
As for any symmetric space the tangent space to Siegel upper-half space is endowed with an operation coming from the Lie bracket on the Lie algebra. We consider the pull-back of this operation to the moduli space of curves via the Torelli…
We establish versions of Szeg\H{o}'s distance formula and Widom's theorem on invertibility of (a family of) Toeplitz operators in a class of finite codimension subalgebras of uniform algebras, obtained by imposing a finite number of linear…
We develop, as the first of a six-paper series, an operator-algebraic framework relating non-relativistic quantum mechanics and special relativity. Three structural facts organize the framework. (i)~The photon sector of free QED is a…
The purpose of this article is to give another molecular decomposition for members of the weighted Hardy spaces.