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CATEGORIES:Applied and Computational Analysis
SUMMARY:Inversion formulae for the cosh-weighted Hilbert t
 ransform - Alexander Tovbis (Dep. of Mathematics U
 niversity of Central Florida)
DTSTART;TZID=Europe/London:20121206T150000
DTEND;TZID=Europe/London:20121206T160000
UID:TALK41308AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/41308
DESCRIPTION:We develop formulae for inverting the so-called co
 sh-weighted Hilbert transform H_μ\, which arises i
 n Single Photon Emission Computed Tomography (SPEC
 T). The formulae are theoretically exact\, require
  the\nminimal amount of data\, and are similar to 
 the classical inversion formulae for the finite Hi
 lbert transform (FHT) H = H_0. We also find the nu
 ll-space and the range of H_μ in L_p with p > 1. S
 imilarly to the FHT\, the null-space turns out to 
 be one-dimensional in L^p for any p in (1\,2)\, an
 d trivial for p ≥ 2. We prove that H_μ is a Fredho
 lm operator when it acts between the L_p spaces\, 
 p in (1\,∞)\, p not equal to 2. Finally\, in the c
 ase p = 2 we find the range condition for H_μ\, wh
 ich is similar to that for the FHT H_0. Our work i
 s based on the method of Riemann-Hilbert problem.\
 nThis is joint work with M. Bertola and A. Katsevi
 ch\, accepted in Proceedings of the AMS
LOCATION:MR 14\, CMS
CONTACT:Carola-Bibiane Schoenlieb
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