Related papers: A matrix application of quasi-monotone sequences t…
We present a super-high-efficiency approximate computing scheme for series sum and discrete Fourier transform. The summation of a series sum or a discrete Fourier transform is approximated by summing over part of the terms multiplied by…
This work introduces a general theory of universal pseudomorphisms and develops their connection to diagrammatic coherence. The main results give hypotheses under which pseudomorphism coherence is equivalent to the coherence theory of…
We survey some recent progress on rigorously establishing the universality of various spectral statistics of Wigner random matrix ensembles, focusing in particular on the Four Moment Theorem and its applications.
The quantum Fourier transform (QFT) is a fundamental primitive in quantum computation and quantum information. In this work, we generalize the QFT for finite groups to a QFT for finite-dimensional semisimple algebras, and give efficient…
In this note a general approach is suggested for comparison of operators. This is done by means of the Fourier transform of a measure. This approach is applied to comparison of approximation properties of various summability methods of the…
We introduce a certain class of summability methods on $L^{\infty}([1, \infty))$ which is defined by convolution in the group algebra $L^1(\mathbb{R}^{\times})$. This class contains an integral version of Ces\`{a}ro summability method and…
We characterise those real analytic mappings between any pair of tori which carry absolutely convergent Fourier series to uniformly convergent Fourier series via composition. We do this with respect to rectangular summation. We also…
In this paper we introduce the new class of generalized Volterra functions. We prove some integral representations for them via Fox-Wright H-functions and Meijer G-functions. From positivity conditions on the weight in these…
In this paper, we study variants of weight enumerators of linear codes over $\mathbb{F}_q$. We generalize the concept of average complete joint weight enumerators of two linear codes over $\mathbb{F}_q$. We also give its MacWilliams type…
A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.
We prove orthogonality relations for some analogs of trigonometric functions on a $q$-quadratic grid and introduce the corresponding $q$-Fourier series. We also discuss several other properties of this basic trigonometric system and the…
It is proved a BMO-estimation for rectangular partial sums of two-dimensional Walsh-Fourier series from which it is derived an almost everywhere exponential summability of rectangular partial sums of double Walsh-Fourier series.
Quasi-Monte Carlo (QMC) rules $1/N \sum_{n=0}^{N-1} f(\boldsymbol{y}_n A)$ can be used to approximate integrals of the form $\int_{[0,1]^s} f(\boldsymbol{y} A) \,\mathrm{d} \boldsymbol{y}$, where $A$ is a matrix and $\boldsymbol{y}$ is row…
We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for…
In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the Laplace operator. The sufficient conditions for summability is obtained. For the orders of Riesz means, which greater…
This article provides a gentle introduction for a general mathematical audience to the factorization theory of motion polynomials and its application in mechanism science. This theory connects in a rather unexpected way a seemingly abstract…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…
Two emergent properties in aggregation theory are investigated, namely horizontal maxitivity and comonotonic maxitivity (as well as their dual counterparts) which are commonly defined by means of certain functional equations. We completely…
We introduce the concept of quotient-convergence for sequences of submodular set functions, providing, among others, a new framework for the study of convergence of matroids through their rank functions. Extending the limit theory of…
We estimate the truncated double trigonometric series $\sum_{n=0}^{N}\sum_{m=0}^{M}a_{mn} {e}^{2\pi \imath \left(m x+n y\right)}$, $a_{mn} \in\mathbb{C}$, in Lebesgue spaces with mixed norms in terms of the $p^{th}-q^{th}$ power finite…