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Fourier transform of surface–carried measures of two-dimensional generic surfaces and applications

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    * Corresponding author 

The second author was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)–Project-ID 258734477–SFB 1173

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  • We give a simple proof of the sharp decay of the Fourier-transform of surface-carried measures of two-dimensional generic surfaces. The estimates are applied to prove Strichartz and resolvent estimates for elliptic operators whose characteristic surfaces satisfy the generic assumptions. We also obtain new results on the spectral and scattering theory of discrete Schrödinger operators on the cubic lattice.

    Mathematics Subject Classification: Primary: 42B20; Secondary: 35R02, 81Q05, 39A12, 35L05.

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  • Figure 1.  Pentagonal region, within which strong $L^p$-$L^q$-Fourier restriction extension estimates hold

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