Related papers: Quarkonial analysis
In this paper, we study the quaternionic counterpart of complex Fock spaces $\mathfrak{F}_{\alpha}^p ( 0<p<\infty$ and for some parameter $\alpha$) of entire slice hyperholomorphic functions in an Euclidean unit ball $\mathbb{B}^n$ in…
Complex functions $\chi (m)$ where $m$ belongs to a Galois field $GF(p^ \ell)$, are considered. Fourier transforms, displacements in the $GF(p^ \ell) \times GF(p^ \ell)$ phase space and symplectic $Sp(2,GF(p^ \ell))$ transforms of these…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
The new approach to decays of heavy quarkonia, based on factorization and expansions in powers of the relative velocity of the valence quarks is reviewed.
Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by…
We study polynomial and exponential stability for $C_{0}$-semigroups using the recently developed theory of operator-valued $(L^{p},L^{q})$ Fourier multipliers. We characterize polynomial decay of orbits of a $C_{0}$-semigroup in terms of…
We derive atomic decompositions and frames for weighted Bergman spaces of several complex variables on the unit ball in the spirit of Coifman, Rochberg, and Luecking. In contrast to our predecessors, we use group theoretic methods, in…
We show that B-spline quarks and the associated quarklets fit into the theory of biorthogonal multiwavelets. Quark vectors are used to define sequences of subspaces $ V_{p,j} $ of $ L_{2}(\mathbb{R}) $ which fulfill almost all conditions of…
Suppose $p \geq 1$ is a computable real. We extend previous work of Clanin, Stull, and McNicholl by classifying the computable $L^p$ spaces whose underlying measure spaces are atomic but not purely atomic. In addition, we determine the…
Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…
In this paper, we establish an analytic version of critical spaces $Q_{\alpha}^{\beta}(\mathbb{R}^{n})$ on unit disc $\mathbb{D}$, denoted by $Q^{\beta}_{p}(\mathbb{D})$. Further we prove a relation between $Q^{\beta}_{p}(\mathbb{D})$ and…
General properties of new models of the electronic Fock spaces based on the notion of (p,q)-sheaves are studied. Interrelation between simple sheaves and density operators is established. Explicit expressions for the transformed reduced…
As the density of matter increases, atomic nuclei disintegrate into nucleons and, eventually, the nucleons themselves disintegrate into quarks. The phase transitions (PT's) between these phases can vary from steep first order to smooth…
Quadratic algebras related to the reflection equations are introduced. They are quantum group comodule algebras. The quantum group $F_q(GL(2))$ is taken as the example. The properties of the algebras (center, representations, realizations,…
We show that subsets of $\mathbb{R}^n$ of large enough Hausdorff and Fourier dimension contain polynomial patterns of the form \begin{align*} ( x ,\, x + A_1 y ,\, \dots,\, x + A_{k-1} y ,\, x + A_k y + Q(y) e_n ), \quad x \in…
We introduce a concept of an embedding of a quadratic space in an associative algebra. The general properties of such embeddings are analyzed by linking it to the Clifford algebra. Conversely, there isa simple description of the standard…
A succinct summary is given of the problem of reconciling observation of black hole-like objects with quantum mechanics. If quantum black holes behave like subsystems, and also decay, their information must be transferred to their…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
This is an addition to a series of papers [FL1, FL2, FL3, FL4], where we develop quaternionic analysis from the point of view of representation theory of the conformal Lie group and its Lie algebra. In this paper we develop split…
Fourier Transforms is a first in a series of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such…