Fourier transform of surface-carried measures of two-dimensional generic surfaces and applications. (English) Zbl 1500.42002
Summary: 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.
MSC:
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 35R02 | PDEs on graphs and networks (ramified or polygonal spaces) |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 39A12 | Discrete version of topics in analysis |
| 35L05 | Wave equation |
Keywords:
oscillatory integrals; dispersive and Strichartz estimates; global well-posedness; spectral theoryReferences:
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