Related papers: A new realization of rational functions, with appl…
The (matricial) solution set of a Linear Matrix Inequality (LMI) is a convex basic non-commutative semi-algebraic set. The main theorem of this paper is a converse, a result which has implications for both semidefinite programming and…
Let $A$ be a rational function. For any decomposition of $A$ into a composition of rational functions $A=U\circ V$ the rational function $\widetilde A=V\circ U$ is called an elementary transformation of $A$, and rational functions $A$ and…
A new generalization of multiquadric functions $\phi(x)=\sqrt{c^{2d}+||x||^{2d}}$, where $x\in\mathbb{R}^n$, $c\in \mathbb{R}$, $d\in \mathbb{N}$, is presented to increase the accuracy of quasi-interpolation further. With the restriction to…
The calculation and manipulation of large multi-variable rational functions is a key bottleneck in multi-loop calculations. In these conference proceedings, based on my article [Chawdhry (2023) arXiv:2312.03672], I present a technique to…
A non-iterative method is presented to calculate the closest Wannier functions (CWFs) to a given set of localized guiding functions, such as atomic orbitals, hybrid atomic orbitals, and molecular orbitals, based on minimization of a…
The number of linear independent algebraic relations among elementary symmetric polynomial functions over finite fields is computed. An algorithm able to find all such relations is described. It is proved that the basis of the ideal of…
We consider the problem of characterizing all functions $f$ defined on the set of integers modulo $n$ with the property that an average of some $n$th roots of unity determined by $f$ is always an algebraic integer. Examples of such…
An extension of Marcinkiewicz Interpolation Theorem, allowing intermediate spaces of Orlicz type, is proved. This generalization yields a necessary and sufficient condition so that every quasilinear operator, which maps the set, $S(X,\mu)$,…
We demonstrate that any function $f$ from a finite set $Y$ to itself can be represented linearly. Specifically, we prove the existence of an injective map $j$ from $Y$ into a modular ring $\mathbb{Z}/m\mathbb{Z}$ and a constant $a \in…
Given constants $x, \nu \in \mathbb{C}$ and the space $\mathscr{H}_0$ of entire functions in $\mathbb{C}$ vanishing at $0$, we consider the integro-differential operator $$ \mathfrak{L} = \left ( \frac{x \, \nu(1-\nu)}{1-x} \right ) \;…
In the context of the complex-analytic structure within the unit disk centered at the origin of the complex plane, that was presented in a previous paper, we show that a certain class of non-integrable real functions can be represented…
In image and audio signal classification, a major problem is to build stable representations that are invariant under rigid motions and, more generally, to small diffeomorphisms. Translation invariant representations of signals in…
This paper studies the cardinal interpolation operators associated with the general multiquadrics, $\phi_{\alpha,c}(x) = (\|x\|^2+c^2)^\alpha$, $x\in\mathbb{R}^d$. These operators take the form $$\mathscr{I}_{\alpha,c}\mathbf{y}(x) =…
We construct $p$-adic triple product $L$-functions that interpolate (square roots of) central critical $L$-values in the balanced region. Thus, our construction complements that of M. Harris and J. Tilouine. There are four central critical…
Let the formal power series f in d variables with coefficients in an arbitrary field be a symmetric function decomposed as a series of Schur functions, and let f be a rational function whose denominator is a product of binomials of the form…
We deal with a problem of the reconstruction of any holomorphic function $f$ on the unit ball of $\mathbb{C}^2$ from its restricions on a union of complex lines. We give an explicit formula of Lagrange interpolation's type that is…
It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we…
We first consider the problem of approximating a few eigenvalues of a rational matrix-valued function closest to a prescribed target. It is assumed that the proper rational part of the rational matrix-valued function is expressed in the…
We consider the problem of the computation of $\inf_p \theta p$ over the set of exponent pairs $P \ni p$ under linear constraints for a certain class of objective functions $\theta$. An effective algorithm is presented. The output of the…
We present a complete solution of the WZW model on the supergroup GL(1|1). Our analysis begins with a careful study of its minisuperspace limit (``harmonic analysis on the supergroup''). Its spectrum is shown to contain indecomposable…