Dispersive estimates for dirac operators in dimension three with obstructions at threshold energies

M. Burak Erdoğan, William R. Green, Ebru Toprak

Research output: Contribution to journalArticle

Abstract

We investigate L1 →L dispersive estimates for the three dimensional Dirac equation with a potential. We also classify the structure of obstructions at the thresholds of the essential spectrum as being composed of a two dimensional space of resonances and finitely many eigenfunctions. We show that, as in the case of the Schrodinger evolution, the presence of a threshold obstruction generically leads to a loss of the natural t-3/2 decay rate. In this case we show that the solution operator is composed of a finite rank operator that decays at the rate t-1/2 plus a term that decays at the rate t-3/2.

Original languageEnglish (US)
Pages (from-to)1217-1258
Number of pages42
JournalAmerican Journal of Mathematics
Volume141
Issue number5
DOIs
StatePublished - Oct 2019

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ASJC Scopus subject areas

  • Mathematics(all)

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