Related papers: Some topics concerning harmonic analysis on metric…
The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.
These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.
In this article, we introduce the concept of lexicographic metric space and, after discussing some basic properties of these metric spaces, such as completeness, boundedness, compactness and separability, we obtain a formula for the metric…
The main purpose of this paper is to discuss Hardy type spaces, Bloch type spaces and the composition operators of complex-valued harmonic functions. We first establish a sharp estimate of the Lipschitz continuity of complex-valued harmonic…
A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…
By putting together an abstract view on quantum mechanics and a quantum-optics picture of the interactions of an atom with light, we develop a corresponding set of C++ classes that set up the numerical analysis of an atom with an arbitrary…
In this paper, we discuss three short topics related to the parity operator and his role in quantum harmonic analysis. We derive results for the Fredholm index of even and odd operators, discuss operators on which the modulation action acts…
In this paper, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The main use of the metric is to compare estimates of trajectories from different…
These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.
Dimensional metrology and positioning operations are used in many fields of particle accelerator projects. This lecture gives the basic tools to designers in the field of measure by analysing the spatial layout of measurement systems since…
This paper presents an overview of close parallels that exist between the theory of positive operator-valued measures (POVMs) associated with a separable Hilbert space and the theory of frames on that space, including its most important…
In this paper we obtain some results of harmonic analysis on quantum complex hyperbolic spaces. We introduce a quantum analog for the Laplace-Beltrami operator and its radial part. The latter appear to be second order $q$-difference…
Hilbert space operators may be mapped onto a space of ordinary functions (operator symbols) equipped with an associative (but noncommutative) star-product. A unified framework for such maps is reviewed. Because of its clear probabilistic…
The first aim of this study is to define soft sequential compact metric spaces and to investigate some important theorems on soft sequential compact metric space. Second is to introduce net and totally bounded soft metric space and study…
We develop a theory of quantum harmonic analysis on lattices in $\mathbb{R}^{2d}$. Convolutions of a sequence with an operator and of two operators are defined over a lattice, and using corresponding Fourier transforms of sequences and…
This is a continuation of our previous work in bi-free harmonic analysis for commuting left and right variables. Here we analyze the bi-free partial S-transform and use the results to study limit theorems and infinite divisibility relative…
We investigate the generation of nonlinear operators with single photon sources, linear optical elements and appropriate measurements of auxiliary modes. We provide a framework for the construction of useful single-mode and two-mode quantum…
This paper reviews some of our recent results in nonlinear atom optics. In addition to nonlinear wave-mixing between matter waves, we also discuss the dynamical interplay between optical and matter waves. This new paradigm, which is now…
The main goal of this paper is to discuss the recent advancements of operator means for accretive matrices in a more general setting. In particular, we present the general form governing the well established definition of geometric mean,…
This is a survey of the recent results and unsolved problems about locally compact homogeneous metric spaces. Mostly, homogeneous finite-dimensional $ANR$-spaces are discussed.