We study the middle convolution of local systems in the setting of singular and étale cohomology. We give a motivic interpretation of the middle convolution in the étale case and prove an independence-of-`-result which yields a description of the determinant. We employ these methods to realize special linear groups regularly as Galois groups over Q(t). In an appendix to this article, written jo...

The semi-discrete convolution with the box spline is an important tool in approximation theory. We give a formula for the difference between semidiscrete convolution and convolution with the box spline. This formula involves multiple Bernoulli polynomials. 1. Box splines and semi-discrete convolution Let V be a n-dimensional real vector space equipped with a lattice Λ. If we choose a basis of t...

Let X be a complex Banach space, be bounded functions, and suppose that the singular points of the Laplace transforms of T and f do not coincide. Under various supplementary assumptions, we show that the convolution T f is bounded. When T(t) = I, this is a classical result of Ingham. Our results are applied to mild solutions of inhomogeneous Cauchy problems on R + : u 0 (t) = Au(t) + f(t) (t 0)...

It easy to see that every bounded linear operator is continuous. It is not hard to show that the converse is also true. The notions of bounded and continuous thereby coincide for linear operators acting between normed spaces. It is customary to prefer the terminology bounded linear operator over that of continuous linear operator. The reason for this preference is the fact that the hard part of...

It is shown that if { p j } is a discrete density function on the integers with support contained in {0 , 1 , ... , d }, and p 0 > 0, p 1 > 0, p d − 1 > 0, p d > 0, then there is an n 0 such that the n-fold convolution { p j } *n is unimodal for all n ≥ n 0 . Examples show that this result is nearly best possible, but weaker results are proved under less restrictive assumptions. On the Unimodal...

In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad ‎et al., ‎‎[K. Maleknejad ‎and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, ‎Appl. Math. Comput.‎ (2005)]‎ to gain...

This paper, introduces a new lter bank structure called the perfect reconstruction circular convolution (PRCC) lter bank. These lter banks satisfy the perfect reconstruction properties, namely, the paraunitary properties in the discrete frequency domain. We further show how the PRCC analysis and synthesis lter banks are completely implemented in this domain and give a simple and a exible method...

We present a fourth order numerical solution method for the singular Neumann boundary problem of Poisson equations. Such problems arise in the solution process of incompressible Navier–Stokes equations and in the time-harmonic wave propagation in the frequence space with the zero wavenumber. The equation is first discretized with a fourth order modified Collatz difference scheme, producing a si...