E. Talvila

activity

20012004

collaborators

9 papers

math.CA2004

Estimates of the remainder in Taylor's theorem using the Henstock--Kurzweil integral

Erik Talvila

When a real-valued function of one variable is approximated by its $n^{t h}$ degree Taylor polynomial, the remainder is estimated using the Alexiewicz and Lebesgue $p$ -norms in case…

math.CA2004

Estimates of Henstock--Kurzweil Poisson integrals

Erik Talvila

If $f$ is a real-valued function on $[- π, π]$ that is Henstock--Kurzweil integrable, let $u_{r} (θ)$ be its Poisson integral. It is shown that $∥ u_{r} ∥_{p} = o (1/ (1 - r))$ as $r \to 1$ and th…

math.CA2003

A product convergence theorem for Henstock--Kurzweil integrals

Parasar Mohanty, Erik Talvila

Necessary and sufficient for $\int_{a}^{b} f g_{n} \to \int_{a}^{b} f g$ for all Henstock--Kurzweil integrable functions $f$ is that $g$ be of bounded variation, $g_{n}$ be uniformly bounded and of…

math.CA2002

Henstock--Kurzweil Fourier transforms

Erik Talvila

The Fourier transform is considered as a Henstock--Kurzweil integral. Sufficient conditions are given for the existence of the Fourier transform and necessary and sufficient condit…

math.CA2001

Sharp Growth Estimates for Modified Poisson Integrals in a Half Space

David Siegel, Erik Talvila

For continuous boundary data, including data of polynomial growth, modified Poisson integrals are used to write solutions to the half space Dirichlet and Neumann problems in $\math…

math.CA2001

Covering theorems and Lebesgue integration

Peter A. Loeb, Erik Talvila

This paper shows how the Lebesgue integral can be obtained as a Riemann sum and provides an extension of the Morse Covering Theorem to open sets. Let $X$ be a finite dimensional no…