Related papers: Sampling theorem associated with q-Dirac system
We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…
Symplectic unitary representations for the Poincar\'{e} group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space…
Mathematical diffraction theory is concerned with the analysis of the diffraction measure of a translation bounded complex measure $\omega$. It emerges as the Fourier transform of the autocorrelation measure of $\omega$. The mathematically…
We prove an analytic KAM-Theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the…
We examine the $q$-Pell sequences and their applications to weighted partition theorems and values of $L$-functions. We also put them into perspective with sums of tails.
The additivity theorem for derivateurs associated to complicial biWaldhausen categories is proved. Also, to any exact category in the sense of Quillen a K-theory space is associated. This K-theory is shown to satisfy the additivity,…
The theory of substitution sequences and their higher-dimensional analogues is intimately connected with symbolic dynamics. By systematically studying the factors (in the sense of dynamical systems theory) of a substitution dynamical…
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…
In the first part of the paper we give a definition of G_q-function and we establish a regularity result, obtained as a combination of a q-analogue of the Andre'-Chudnovsky Theorem [And89, VI] and Katz Theorem [Kat70, \S 13]. In the second…
Due to the advances in the manufacturing of quantum hardware in the recent years, significant research efforts have been directed towards employing quantum methods to solving problems in various areas of interest. Thus a plethora of novel…
The $p$-adic $q$-integral (= $I_q$-integral) was defined by author in the previous paper [1, 3]. In this paper, we consider $I_q$-Fourier transform and investigate some properties which are related to this transform.
We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. First, we study the…
Selecting optimal kernels for regression in physical systems remains a challenge, often relying on trial-and-error with standard functions. In this work, we establish a mathematical correspondence between support vector machine kernels and…
We briefly review the overlap formalism for chiral gauge theories, the overlap Dirac operator for massless fermions and its connection to domain wall fermions. We describe properties of the overlap Dirac operator, and methods to implement…
A semiclassical model is presented for characterizing the linear response of elementary quantum optical systems involving cavities, optical fibers, and atoms. Formulating the transmission and reflection spectra using a scattering-wave…
We present the first representation of the general term of the Rayleigh-Schr\"odinger series for quasidegenerate systems. Each term of the series is represented by a tree and there is a straightforward relation between the tree and the…
A logical system derived from linear logic and called QMLL is introduced and shown able to capture all unitary quantum circuits. Conversely, any proof is shown to compute, through a concrete GoI interpretation, some quantum circuits. The…
The article considers some concrete solutions to the Dirac equation coupled to a vector bundle with connection, arising in the study of Yang-Mills equations and vector bundles on Riemann surfaces.
In this survey paper we discuss some tools and methods which are of use in quasi-Monte Carlo (QMC) theory. We group them in chapters on Numerical Analysis, Harmonic Analysis, Algebra and Number Theory, and Probability Theory. We do not…
This work focuses on the invariance of important properties between continuous and discrete models of systems which can be useful in the control design of large-scale systems and their software implementations. In particular, this paper…