Related papers: Quarkonial analysis
We construct atomic decompositions for crystals of type $C_{2}$ and define a charge statistic on them, thus providing positive combinatorial formulas for Kostka-Foulkes polynomials associated to them together with a natural geometric…
A full characterization of $(p,q)$-deformed Fibonacci and Lucas polynomials is given. These polynomials obey non-conventional three-term recursion relations. Their generating functions and Fourier integral transforms are explicitly computed…
Affine forms are a common way to represent convex sets of $\mathbb{R}$ using a base of error terms $\epsilon \in [-1, 1]^m$. Quadratic forms are an extension of affine forms enabling the use of quadratic error terms $\epsilon_i \epsilon_j$.…
In this note, we provide some categorical perspectives on the relativization construction arising from quantum measurement theory in the presence of symmetries and occupying a central place in the operational approach to quantum reference…
First some old as well as new results about P.I. algebras, Ore extensions, and degrees are presented. Then quantized $n\times r$ matrices as well as quantized factor algebras of $M_q(n)$ are analyzed. The latter are the quantized function…
A new application of quantum field theory is developed that gives a description of the internal dynamics of dressed elementary particles and predicts their masses. The fermionic and bosonic quantum fields are treated as interdependent…
Spectral Barron spaces, constituting a specialized class of function spaces that serve as an interdisciplinary bridge between mathematical analysis, partial differential equations (PDEs), and machine learning, are distinguished by the decay…
Bifractional displacement operators, are introduced by performing two fractional Fourier transforms on displacement operators. They are shown to be special cases of elements of the group G, that contains both displacements and squeezing…
The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…
Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation…
We obtain some simple relations between decomposition numbers of quantized Schur algebras at an n-th root of unity (over a field of characteristic 0). These relations imply that every decomposition number for such an algebra occurs as a…
This article deals with harmonic analysis on affine buildings. Its main goal is to construct suitable kernels associated to a discrete multitemporal wave equations on the latter spaces, the long-standing motivation being to contribute to…
The Hawking minisuperspace model (closed FRW geometry with a homogeneous massive scalar field) provides a fairly non-trivial testing ground for fundamental problems in quantum cosmology. We provide evidence that the Wheeler-DeWitt equation…
This paper initiates a systematic study of operators arising as integrals of operator-valued functions with respect to positive operator-valued measures and utilizes these tools to provide relativization maps (Yen) for quantum reference…
This work starts with the introduction of a family of differential energy operators. Energy operators ($Psi_R^+$, $Psi_R^-$) were defined together with a method to decompose the wave equation in a previous work. Here the energy operators…
We consider the linear vector space formed by the elements of the finite fields $\mathbb{F}_q$ with $q=p^r$ over $\mathbb{F}_p$. Let ${a_1,\ldots,a_r}$ be a basis of this space. Then the elements $x$ of $\mathbb{F}_q$ have a unique…
Given a dilation matrix M, a so-called space of M-positive vectors in the Euclidean space is introduced and studied. An algebraic structure of this space is similar to the positive half-line equipped with the termwise addition modulo 2,…
In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution…
Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The…
A brief review of the search for variation of the fine structure constant in quasar absorption spectra is presented. Special consideration is given to the role of atomic calculations in the analysis of the observed data. A range of methods…