Year: 2011
Type: article
Abstract: This paper gives three theorems regarding functions integrable on $[-1,1]$ with respect to Jacobi weights and having nonnegative coefficients in their (Fourier–)Jacobi expansions. We show that the $L^p$-integrability (with respect to the Jacobi weight) on an interval near $1$ implies the $L^p$-integrability on the whole interval if $p$ is an even integer. The Jacobi expansion of a function locally in $L^\infty$ near $1$ is shown to converge uniformly and absolutely on $[-1,1]$; in particular, such a function is shown to be continuous on $[-1,1]$. Similar results are obtained for functions in local Besov approximation spaces.
Authors: H. N. Mhaskar, S. Tikhonov
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2005227880