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arXiv · 1310.8074

Sharp decay estimates in Lorentz spaces for nonnegative Schrödinger heat semigroups

Norisuke Ioku·Kazuhiro Ishige·Eiji Yanagida
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Abstract

Let $H:=-Δ+V$ be a nonnegative Schrödinger operator on $L^2({\bf R}^N)$, where $N\ge 2$ and $V$ is a radially symmetric function decaying quadratically at the space infinity. In this paper we consider the Schrödinger heat semigroup $e^{-tH}$, and make a complete table of the decay rates of the operator norms of $e^{-tH}$ in the Lorentz spaces as $t\to\infty$.

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Norisuke Ioku, Kazuhiro Ishige, Eiji Yanagida. 2013-10-30. Sharp decay estimates in Lorentz spaces for nonnegative Schrödinger heat semigroups. https://arxiv.org/abs/1310.8074

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