Asymptotic Analysis of Diffraction Integrals in Gevrey Spaces

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• 作者：Franco Cardin (1)
  Todor Gramchev (2)
  Alberto Lovison (1)
  
• 关键词：Oscillatory integrals ; Caustics ; Asymptotics in Gevrey spaces ; 41A60 ; 58J37 ; 78A05 ; 58C28
• 刊名：Acta Applicandae Mathematicae
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：132
• 期：1
• 页码：177-187
• 全文大小：1,009 KB
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• 作者单位：Franco Cardin (1)
  Todor Gramchev (2)
  Alberto Lovison (1)
  
  1. Dipartimento di Matematica, Universit脿 degli Studi di Padova, Via Trieste, 63, 35121, Padova, Italy
  2. Dipartimento di Matematica e Informatica, Universit脿 di Cagliari, Via Ospedale, 72, 09124, Cagliari, Italy
  
• ISSN：1572-9036

文摘

We present an overview on the state of the art of the research on the asymptotic behavior of diffraction integrals, i.e., the oscillatory integrals employed in the Fresnel theory of optics. We focus on the behavior of such integrals in the presence of standard caustics, in particular the elliptic and the hyperbolic umbilics, adopting the functional setting of Gevrey spaces. We also derive new estimates for the shadow region of the hyperbolic umbilic in terms of the distance from the caustic under symmetry condition in the space of parameters.