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• W2059603411 startingPage "1936" @default.
• W2059603411 abstract "We investigate $L^1(mathbb R^4)to L^infty(mathbb R^4)$ dispersive estimates for the Schrodinger operator $H=-Delta+V$ when there are obstructions, a resonance or an eigenvalue, at zero energy. In particular, we show that if there is a resonance or an eigenvalue at zero energy then there is a time dependent, finite rank operator $F_t$ satisfying $|F_t|_{L^1to L^infty} lesssim 1/log t$ for $t>2$ such that $$|e^{itH}P_{ac}-F_t|_{L^1to L^infty} lesssim t^{-1},,,,,,text{for} t>2.$$ We also show that the operator $F_t=0$ if there is an eigenvalue but no resonance at zero energy. We then develop analogous dispersive estimates for the solution operator to the four dimensional wave equation with potential." @default.
• W2059603411 created "2016-06-24" @default.
• W2059603411 creator A5011150158 @default.
• W2059603411 creator A5017012795 @default.
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• W2059603411 date "2014-08-19" @default.
• W2059603411 modified "2023-10-15" @default.
• W2059603411 title "Dispersive Estimates for Four Dimensional Schrödinger and Wave Equations with Obstructions at Zero Energy" @default.
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• W2059603411 doi "https://doi.org/10.1080/03605302.2014.921928" @default.
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