5 papers · 1 filter
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…
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 be a finite dimensional no…
Rapidly growing Fourier integrals
Erik Talvila
The Riemann-Lebesgue Lemma says that the Fourier transform of an absolutely integrable function on the real line tends to zero as the transform parameter tends to infinity. When th…
Necessary and sufficient conditions for differentiating under the integral sign
Erik Talvila
We give necessary and sufficient conditions for differentiating under the integral sign an integral that depends on a parameter. The conditions require the equality of two iterated…
Some divergent trigonometric integrals
Erik Talvila
Some divergent trigonometric integrals have appeared in standard tables for many years, listed as converging. We give a simple proof that these integrals diverge and trace their hi…