Decay of the Fourier transform of surfaces with vanishing curvature
László Erdös
Salmhofer, Manfred
We prove L p -bounds on the Fourier transform of measures μ supported on two dimensional surfaces. Our method allows to consider surfaces whose Gauss curvature vanishes on a one-dimensional submanifold. Under a certain non-degeneracy condition, we prove that μ ∧ ε L 4+β, β > 0, and we give a logarithmically divergent bound on the L 4-norm. We use this latter bound to estimate almost singular integrals involving the dispersion relation, e(p)= ∑13 [1-\cos p_j]} , of the discrete Laplace operator on the cubic lattice. We briefly explain our motivation for this bound originating in the theory of random Schrödinger operators.
Springer
2007
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http://purl.org/coar/resource_type/c_6501
https://research-explorer.ista.ac.at/record/2752
Erdös L, Salmhofer M. Decay of the Fourier transform of surfaces with vanishing curvature. <i>Mathematische Zeitschrift</i>. 2007;257(2):261-294. doi:<a href="https://doi.org/10.1007/s00209-007-0125-4">10.1007/s00209-007-0125-4</a>
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00209-007-0125-4
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