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

Jean-Claude Cuenin; Robert Schippa

doi:10.3934/cpaa.2022079

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2022, Volume 21, Issue 9: 2873-2889. Doi: 10.3934/cpaa.2022079

This issue Previous Article Next Article Asymptotic behavior of eigenvalues of the Maxwell system in the presence of small changes in the interface of an inclusion

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

Jean-Claude Cuenin^1, , and
Robert Schippa^2,

1.
Loughborough University, Department of Mathematical Sciences, Loughborough, Leicestershire, LE11 3TU United Kingdom
2.
Karlsruher Institut für Technologie, Fakultät für Mathematik, Institut für Analysis, Englerstrasse 2, 76131 Karlsruhe, Germany

^* Corresponding author
^* Corresponding author

Received: January 2022

Revised: March 2022

Early access: April 2022

Published: September 2022

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

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Abstract

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.

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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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