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SUMMARY:Estimation of a 2D Fourier integral for the quarter-plane diffract
 ion problem - Andrey Shanin (Moscow State University)
DTSTART:20230207T114500Z
DTEND:20230207T123000Z
UID:TALK194758@talks.cam.ac.uk
DESCRIPTION:The classical problem of diffraction of a scalar monochromatic
  wave by a Dirichlet thin quarter-plane screen in the 3D space is studied.
  As it is known\, this problem admits separation of variables\, but no ana
 log of the Wiener-Hopf method for it has been built. In [1] we propose an 
 approach enabling one to study the singularities of the solution of the pr
 oblem a priori (i.e. without building the solution). The wave field become
 s represented as a 2D Fourier integral whose transformant has an unknown r
 egular part and an explicitly known singular part. Here we address a techn
 ical but important problem: we reconstruct the principal wave terms from t
 he singularities of the Fourier transformant. As the basic technique\, we 
 use the method developed in [2].\nWe demonstrate that the locality princip
 le is applicable to the integral: the principal wave terms are produced by
  the crossings of the singularity components or the saddle points on the s
 ingularity. After a careful analysis\, we obtain that all components obtai
 ned this way correspond to certain rays.\nThe work is co-authored by R.C.A
 ssier and A.I.Korolkov.\n[1] R.C.Assier\, A.V.Shanin\, Diffraction by a qu
 arter-plane. Analytical continuation of spectral function // QJMAM V. 72\,
  51-85 (2019).\n[2] R.C.Assier\, A.V.Shanin\, A.I.Korolkov\, A contributio
 n to the mathematical theory of diffraction: a note on double Fourier inte
 grals // QJMAM\, DOI: 10.1093/qjmam/hbac017
LOCATION:Seminar Room 1\, Newton Institute
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