Abstract
Slepian, Landau, and Pollak used prolate spheroidal wave functions to demonstrate how nearly “time” and “bandlimited” a square-integrable function can be. In this note we show how their results extend easily to cover orthogonal polynomial expansions. In particular, we study how close a square-integrable function can come to being a polynomial of degree $ \leqq L$ and simultaneously to vanishing off some set $\mathcal{A}$.
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