BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:The Fredholm Factorization Method Directly Applied to Generalized 
 Wiener-Hopf Equations - Guido Lombardi (Politecnico di Torino)
DTSTART:20240704T104500Z
DTEND:20240704T111500Z
UID:TALK214963@talks.cam.ac.uk
DESCRIPTION:Authors: Vito Daniele\, Guido Lombardi\, Politecnico di Torino
 \, Italy\, e-mail: vito.daniele@polito.it\, guido.lombardi@polito.it\n&nbs
 p\;\nIn this work we present a new and comprehensive theory for the soluti
 on of Generalized Wiener-Hopf equations (GWHEs). We recall that GWHEs have
  plus and minus unknowns that are defined into different complex planes bu
 t related together. In particular\, this kind of Wiener-Hopf equations ari
 se while studying diffraction problems from angular regions\, such as in a
 coustics\, electromagnetics and elasticity. The effectiveness of this tech
 nique has already been demonstrated in the analysis of electromagnetic sca
 ttering from wedge problems immersed in isotropic media resorting to solut
 ion methods ranging from closed form factorization to approximate factoriz
 ation called Fredholm factorization technique. The technique is combined w
 ith special complex mapping to transform GWHEs into Classical Wiener-Hopf 
 equations. The same technique has been also extended to mixed types of can
 onical regions i.e. with rectangular an angular shapes.\nWe believe that t
 his mathematical technique significantly expands the possibilities for spe
 ctral analysis of problems involving angular regions filled with complex a
 rbitrary linear media\, in particular in electromagentics. We observe that
  the GWHEs in arbitrary linear media usually report physical unknowns defi
 ned into multiple complex planes (more than 2) as the physical problem usu
 ally contains more than one propagation constant. Traditional effective sp
 ectral methods to study diffraction problem such as Sommerfeld-Malyuzhinet
 s (SM) method and the Kontorovich-Lebedev (KL) takes benefit from the use 
 of spectral complex angular plane derived from the Sommerfeld integral the
 ory\, which has also been successfully applied in the Generalized Wiener-H
 opf method. However\, the definition of this complex plane is possible in 
 problem with one propagation constant.\nIn the present work\, we apply for
  the first times direct Fredholm factorization to GWHEs avoiding introduct
 ion of spectral mapping. In particular the method is effective for problem
 s with more than one propagation constant where the spectral mapping canno
 t be introduced\, and other techniques are ineffective.\nDuring the presen
 tation we will show the effectiveness of applying the technique and its ge
 nerality.\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR