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- University of SaskatchewanCA19 papers
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8 papers · 1 filter
Fourier transform inversion using an elementary differential equation and a contour integral
Erik Talvila
Let be a function on the real line. The Fourier transform inversion theorem is proved under the assumption that is absolutely continuous such that and are Lebesgue…
The primitive integral
Erik Talvila
For each a space of integrable Schwartz distributions, $L^'^{\,p}$, is defined by taking the distributional derivative of all functions in . Here, is wi…
Simple derivation of basic quadrature formulas
Erik Talvila, Matthew Wiersma
Simple proofs of the midpoint, trapezoidal and Simpson's rules are proved for numerical integration on a compact interval. The integrand is assumed to be twice continuously differe…
Integrals and Banach spaces for finite order distributions
Erik Talvila
Let $\Bc$ denote the real-valued functions continuous on the extended real line and vanishing at . Let $\Br$ denote the functions that are left continuous, have a right li…
Fourier series with the continuous primitive integral
Erik Talvila
Fourier series are considered on the one-dimensional torus for the space of periodic distributions that are the distributional derivative of a continuous function. This space of di…
Convolutions with the continuous primitive integral
Erik Talvila
If is a continuous function on the real line and is its distributional derivative then the continuous primitive integral of distribution is . Th…