Dispersion for Schrödinger operators on regular trees

Kaïs Ammari; Mostafa Sabri

doi:10.1007/s13324-022-00664-y

Dispersion for Schrödinger operators on regular trees

Kaïs Ammari, Mostafa Sabri

Science

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

Abstract

We prove dispersive estimates for two models: the adjacency matrix on a discrete regular tree, and the Schrödinger equation on a metric regular tree with the same potential on each edge/vertex. The latter model can be thought of as an extension of the case of periodic Schrödinger operators on the real line. We establish a t^{- 3 / 2}-decay for both models which is sharp, as we give the first-order asymptotics.

Original language	English (US)
Article number	56
Journal	Analysis and Mathematical Physics
Volume	12
Issue number	2
DOIs	https://doi.org/10.1007/s13324-022-00664-y
State	Published - Apr 2022

Keywords

Dispersion
Graphs
Quantum graphs
Stationary phase
Trees

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Mathematical Physics

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10.1007/s13324-022-00664-y

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abstract = "We prove dispersive estimates for two models: the adjacency matrix on a discrete regular tree, and the Schr{\"o}dinger equation on a metric regular tree with the same potential on each edge/vertex. The latter model can be thought of as an extension of the case of periodic Schr{\"o}dinger operators on the real line. We establish a t- 3 / 2-decay for both models which is sharp, as we give the first-order asymptotics.",

keywords = "Dispersion, Graphs, Quantum graphs, Stationary phase, Trees",

author = "Ka{\"i}s Ammari and Mostafa Sabri",

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AB - We prove dispersive estimates for two models: the adjacency matrix on a discrete regular tree, and the Schrödinger equation on a metric regular tree with the same potential on each edge/vertex. The latter model can be thought of as an extension of the case of periodic Schrödinger operators on the real line. We establish a t- 3 / 2-decay for both models which is sharp, as we give the first-order asymptotics.

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KW - Graphs

KW - Quantum graphs

KW - Stationary phase

KW - Trees

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ER -

Dispersion for Schrödinger operators on regular trees

Abstract

Keywords

ASJC Scopus subject areas

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