Sharp decay estimates in Lorentz spaces for nonnegative Schrödinger heat semigroups

Norisuke Ioku; Kazuhiro Ishige; Eiji Yanagida

doi:10.1016/j.matpur.2014.09.006

Sharp decay estimates in Lorentz spaces for nonnegative Schrödinger heat semigroups

Norisuke Ioku, Kazuhiro Ishige, Eiji Yanagida

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

Let H:=-δ+V be a nonnegative Schrödinger operator on L²(R^N), where N≥2 and V be 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→∞.

Original language	English
Pages (from-to)	900-923
Number of pages	24
Journal	Journal des Mathematiques Pures et Appliquees
Volume	103
Issue number	4
DOIs	https://doi.org/10.1016/j.matpur.2014.09.006
Publication status	Published - 2015 Apr 1

Keywords

Lorentz spaces
Quadratically decaying potential
Schrödinger heat semigroups

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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title = "Sharp decay estimates in Lorentz spaces for nonnegative Schr{\"o}dinger heat semigroups",

abstract = "Let H:=-δ+V be a nonnegative Schr{\"o}dinger operator on L2(RN), where N≥2 and V be a radially symmetric function decaying quadratically at the space infinity. In this paper we consider the Schr{\"o}dinger 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→∞.",

keywords = "Lorentz spaces, Quadratically decaying potential, Schr{\"o}dinger heat semigroups",

author = "Norisuke Ioku and Kazuhiro Ishige and Eiji Yanagida",

note = "Funding Information: The second author was supported in part by the Grant-in-Aid for Scientific Research (B) (No. 23340035 ) from Japan Society for the Promotion of Science . The third author was supported in part by Grant-in-Aid for Scientific Research (A) (No. 24244012 ) from Japan Society for the Promotion of Science . ",

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doi = "10.1016/j.matpur.2014.09.006",

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T1 - Sharp decay estimates in Lorentz spaces for nonnegative Schrödinger heat semigroups

AU - Ioku, Norisuke

AU - Ishige, Kazuhiro

AU - Yanagida, Eiji

N1 - Funding Information: The second author was supported in part by the Grant-in-Aid for Scientific Research (B) (No. 23340035 ) from Japan Society for the Promotion of Science . The third author was supported in part by Grant-in-Aid for Scientific Research (A) (No. 24244012 ) from Japan Society for the Promotion of Science .

PY - 2015/4/1

Y1 - 2015/4/1

N2 - Let H:=-δ+V be a nonnegative Schrödinger operator on L2(RN), where N≥2 and V be 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→∞.

AB - Let H:=-δ+V be a nonnegative Schrödinger operator on L2(RN), where N≥2 and V be 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→∞.

KW - Lorentz spaces

KW - Quadratically decaying potential

KW - Schrödinger heat semigroups

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