Derivatives of L^p eigenfunctions of Schrodinger operators

Details Derivatives of L^p eigenfunctions of Schrodinger operators Derivatives of L^p eigenfunctions of Schrodinger operators

2011-12-15

arxiv.org/abs/1112.3673v1

Mathematics

Spectral Theory

7 pages

Scientific paper

Assuming the negative part of the potential is uniformly locally $L^1$, we
prove a pointwise $L^p$ estimate on derivatives of eigenfunctions of
one-dimensional Schrodinger operators. In particular, if an eigenfunction is in
$L^p$, then so is its derivative, for $1\le p\le \infty$.

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