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• W2963260219 abstract "We investigate dispersive estimates for the Schrödinger operator $H=-Delta +V$ with $V$ is a real-valued decaying potential when there are zero energy resonances and eigenvalues in four spatial dimensions. If there is a zero energy obstruction, we establish the low-energy expansion begin{align*} e^{itH}chi(H) P_{ac}(H) & =O(frac 1{log t}) A_0+ O(frac 1 t )A_1+O((tlog t)^{-1})A_2 & + O(t^{-1}(log t)^{-2})A_3. end{align*} Here, $A_0,A_1:L^1(mathbb R^4)to L^infty (mathbb R^4)$, while $A_2,A_3$ are operators between logarithmically weighted spaces, with $A_0,A_1,A_2$ finite rank operators, further the operators are independent of time. We show that similar expansions are valid for the solution operators to Klein-Gordon and wave equations. Finally, we show that under certain orthogonality conditions, if there is a zero energy eigenvalue one can recover the $|t|^{-2}$ bound as an operator from $L^1to L^infty$. Hence, recovering the same dispersive bound as the free evolution in spite of the zero energy eigenvalue." @default.
• W2963260219 created "2019-07-30" @default.
• W2963260219 creator A5049644755 @default.
• W2963260219 creator A5069727861 @default.
• W2963260219 date "2017-05-01" @default.
• W2963260219 modified "2023-10-18" @default.
• W2963260219 title "Decay estimates for four dimensional Schrödinger, Klein-Gordon and wave equations with obstructions at zero energy" @default.
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• W2963260219 doi "https://doi.org/10.57262/die/1489802418" @default.
• W2963260219 hasPublicationYear "2017" @default.
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