Related papers: A note on Sonnenschein summability matrices

Fourier series with absolutely summable coefficients provide a classical example of a commutative Banach algebra, and these notes are concerned with this and related matters.

An analytical solution for the optical efficiency of a luminescent solar concentrator is presented. Due to a large number of input parameters and their complex effect on the device efficiency numerical simulations have been previously used…

In this paper we describe a method of calculation of master integrals based on the solution of systems of difference equations in one variable. Various explicit examples are given, as well as the generalization to arbitrary diagrams.

We utilize the trip matrix method of calculating the Jones Polynomial to give an alternative proof that the Jones Polynomial is multiplicative under connect sums.

Analogous to the sl(n) case, we address the computation of the index of seaweed subalgebras of sp(2n) by introducing graphical representations called symplectic meanders. Formulas for the algebra's index may be computed by counting the…

Jacobi sums and cyclotomic numbers are the important objects in number theory. The determination of all the Jacobi sums and cyclotomic numbers of order $e$ are merely intricate to compute. This paper presents the lesser numbers of Jacobi…

A simple recursive scheme for parameterisation of n-by-n unitary matrices is presented.

In this paper, we present the foundations of Summability Calculus, which places various established results in number theory, infinitesimal calculus, summability theory, asymptotic analysis, information theory, and the calculus of finite…

This paper gives new explicit formulas for sums of powers of integers and their reciprocals.

A general method for calculating asymptotic expansions of infinite sums in thermal field theory is presented. It is shown that the Mellin summation method works elegantly with dimensional regularization. A general result is derived for a…

The sum formula is a well known relation in the field of the multiple zeta values. In this paper, we present its generalization for the Euler-Zagier multiple zeta function.

In this paper, we give estimates for both upper and lower bounds of eigenvalues of a simple matrix. The estimates are shaper than the known results.

The goal of this note is to present a combinatorial mechanism for counting certain objects associated to a variety X defined over a finite field. The basic example is that of counting conjugacy classes in GL_n(F_q), where X is the…

We compute the spectrum of the "all ones" hypermatrix using the Poisson product formula. This computation includes a complete description of the eigenvalues' multiplicities, a seemingly elusive aspect of the spectral theory of tensors. We…

The explicit formulas expressing harmonic sums via alternating Euler sums (colored multiple zeta values) are given, and some explicit evaluations are given as applications.

We establish a simple identity and using it we find a new proof of a result of Kloosterman.

In the space of all entire functions it is solved the problem of interpolation taking into account multiplicities by sums of the series of exponentials with the exponents from a given set. It is found a criterion of solubility of the…

We develop a procedure for determining whether a square complex matrix is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. Our approach has several advantages over existing methods. We discuss these differences and…

We prove a Tauberian theorem for the Voronoi summation method of divergent series with an estimate of the remainder term. The results on the Voronoi summability are then applied to analyze the mean values of multiplicative functions on…

Motivated by connections between minimal actions, especially T\"oplitz, on Cantor sets, and dimension groups, we find realizations of classes of dimension groups as limits of primitive matrices all of which have equal column sums, or equal…