Sets of p-restriction and p-spectral synthesis

• Autorzy: Puls Michael J.

Identyfikatory

DOI

10.1515/dema-2019-0033

• Języki publikacji: EN

Abstrakty

EN

In this paper we investigate the restriction problem. More precisely, we give sufficient conditions for the failure of a set E in Rn to have the p-restriction property. We also extend the concept of spectral synthesis to Lp(Rn) for sets of p-restriction when p > 1. We use our results to show that there are p-values for which the unit sphere is a set of p-spectral synthesis in Rn when n ≥ 3.

Słowa kluczowe

EN

p-spectral synthesis; restriction problem; set of p-restriction; span of translates

PL

synteza spektralna; zbiór restrykcji

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2019
• Tom: Vol. 52, nr 1
• Strony: 397--403
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Puls Michael J.

• Department of Mathematics, John Jay College-CUNY, 524 West 59th Street, New York, NY 10019, USA

Bibliografia

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• [3] Tao T., Some recent progress on the restriction conjecture, In: Brandolini L., Colzani L., Iosevich A., Travaglini G. (Eds.), Fourier analysis and convexity, Appl. Numer. Harmon. Anal., Birkhäuser Boston, Boston, MA, 2004
• [4] Grafakos L., Modern Fourier analysis, volume 250 of Graduate Texts in Mathematics, 3rd ed., Springer, New York, 2014
• [5] Stolyarov D. M., Functions whose Fourier transform vanishes on a surface, 2016, arXiv:1601.04604
• [6] Domar Y., On the spectral synthesis problem for (n – 1)-dimensional subsets of Rn, n ≥ 2, Ark. Mat., 1971, 9, 23-37
• [7] Rudin W., Fourier analysis on groups, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1990
• [8] Herz C. S., Spectral synthesis for the circle, Ann. of Math. (2), 1958, 68(3), 709-712
• [9] Agranovsky M. L., Narayanan E. K., Lp-integrability, supports of Fourier transforms and uniqueness for convolution equations, J. Fourier Anal. Appl., 2004, 10(3), 315-324
• [10] Guo K., On the p-thin problem for hypersurfaces of Rn with zero Gaussian curvature, Canad. Math. Bull., 1993, 36(1), 64-73
• [11] Guo K., On the p-approximate property for hypersurfaces of Rn, Math. Proc. Cambridge Philos. Soc., 1989, 105(3), 503-511
• [12] Guo K., A representation of distributions supported on smooth hypersurfaces of Rn, Math. Proc. Cambridge Philos. Soc.,1995, 117(1), 153-160

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).