{"date_updated":"2021-01-12T06:59:28Z","publist_id":"4140","volume":257,"extern":1,"type":"journal_article","intvolume":"       257","_id":"2752","doi":"10.1007/s00209-007-0125-4","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"László Erdös"},{"last_name":"Salmhofer","first_name":"Manfred","full_name":"Salmhofer, Manfred"}],"quality_controlled":0,"title":"Decay of the Fourier transform of surfaces with vanishing curvature","publication":"Mathematische Zeitschrift","issue":"2","publication_status":"published","abstract":[{"text":"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 &gt; 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.","lang":"eng"}],"citation":{"short":"L. Erdös, M. Salmhofer, Mathematische Zeitschrift 257 (2007) 261–294.","ama":"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>","mla":"Erdös, László, and Manfred Salmhofer. “Decay of the Fourier Transform of Surfaces with Vanishing Curvature.” <i>Mathematische Zeitschrift</i>, vol. 257, no. 2, Springer, 2007, pp. 261–94, doi:<a href=\"https://doi.org/10.1007/s00209-007-0125-4\">10.1007/s00209-007-0125-4</a>.","ieee":"L. Erdös and M. Salmhofer, “Decay of the Fourier transform of surfaces with vanishing curvature,” <i>Mathematische Zeitschrift</i>, vol. 257, no. 2. Springer, pp. 261–294, 2007.","ista":"Erdös L, Salmhofer M. 2007. Decay of the Fourier transform of surfaces with vanishing curvature. Mathematische Zeitschrift. 257(2), 261–294.","chicago":"Erdös, László, and Manfred Salmhofer. “Decay of the Fourier Transform of Surfaces with Vanishing Curvature.” <i>Mathematische Zeitschrift</i>. Springer, 2007. <a href=\"https://doi.org/10.1007/s00209-007-0125-4\">https://doi.org/10.1007/s00209-007-0125-4</a>.","apa":"Erdös, L., &#38; Salmhofer, M. (2007). Decay of the Fourier transform of surfaces with vanishing curvature. <i>Mathematische Zeitschrift</i>. Springer. <a href=\"https://doi.org/10.1007/s00209-007-0125-4\">https://doi.org/10.1007/s00209-007-0125-4</a>"},"month":"01","date_created":"2018-12-11T11:59:25Z","year":"2007","status":"public","publisher":"Springer","page":"261 - 294","day":"01","date_published":"2007-01-01T00:00:00Z"}