Abstract
The results in the present paper are a natural continuation of the arguments in [7], [9] and are also motivated by an attempt to see wether the results in those papers can be improved when stronger assumptions are made. The main theme is to study decay for Fourier tranforms of surface carried densities which live on surfaces with uniplanar and conical singularities.
Keywords: Decay estimates, Fourier transforms, Surfaces with singular points
Similar content being viewed by others
References
1. Bannini, A.: Stime asintotiche di integrali oscillatori ed applicazioni ad equazioni alle derivate parziali iperboliche. Ph.d. thesis, Bologna (2005)
2. Courant, R., Hilbert, D.: Methods of mathematical physics. Volume II: Partial differential equations. Wiley Classics Edition. New York etc.: John Wiley & Sons/Interscience Publishers. xxii, p. 830 (1989)
3. Duff, G.F.D.: The Cauchy problem for elastic waves in an anisotropic medium. Phil. Transactions Royal Soc. London, Ser. A Nr. 1010, Vol. 252, 249–273 (1960)
4. Fedoriuk, M.V.: The saddle point method. (In Russian). Nauka Publ. Comp., Moscow (1977)
5. Hlawka, E.: Über Integrale auf konvexen Körpern. I. Monatsh.Math. 54, 1–36 (1950)
6. Hörmander, L.: The Analysis of Linear Partial Differential Operators,I. Grundlehren Series vol. 256, Springer Verlag, Berlin (1983)
7. Liess, O.: Decay estimates for the solutions of the system of crystal optics. Asymptotic Analysis 4, 61-95 (1991)
8. Liess, O.: Decay estimates for the solutions of the system of crystal acoustics for cubic crystals. Recent Trends in Microlocal Analysis. Kokyoroku series of the RIMS in Kyoto nr. 1412, 1–13 (2005)
9. Liess, O.: Estimates for Fourier transforms of surface-carried densities on surfaces with singular points. Asymptotic analysis 37, 329–363 (2004)
10. Littman, W.: Fourier transforms of surface carried measures and differentiablity of surface averages. Bull. Am. Math. Soc. 69, 766-770 (1963)
11. Musgrave, M.J.P.: Crystal acoustics. Holden and Day, San Francisco (1979)
12. Stein, E.M.: Harmonic analysis: real variable methods, orthogonality, and oscillatory integrals. Princeton University Press, Princeton (1993)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bannini, A., Liess, O. Estimates for Fourier transforms of surface carried densities on surfaces with singular points, II . Ann. Univ. Ferrara 52, 211–232 (2006). https://doi.org/10.1007/s11565-006-0017-2
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11565-006-0017-2