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SUMMARY:Inversion formulae for the cosh-weighted Hilbert transform - Alexa
 nder Tovbis (Dep. of Mathematics University of Central Florida)
DTSTART:20121206T150000Z
DTEND:20121206T160000Z
UID:TALK41308@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:We develop formulae for inverting the so-called cosh-weighted 
 Hilbert transform H_μ\, which arises in Single Photon Emission Computed T
 omography (SPECT). The formulae are theoretically exact\, require the\nmin
 imal amount of data\, and are similar to the classical inversion formulae 
 for the finite Hilbert transform (FHT) H = H_0. We also find the null-spac
 e and the range of H_μ in L_p with p > 1. Similarly to the FHT\, the null
 -space turns out to be one-dimensional in L^p for any p in (1\,2)\, and tr
 ivial for p ≥ 2. We prove that H_μ is a Fredholm operator when it acts 
 between the L_p spaces\, p in (1\,∞)\, p not equal to 2. Finally\, in th
 e case p = 2 we find the range condition for H_μ\, which is similar to th
 at for the FHT H_0. Our work is based on the method of Riemann-Hilbert pro
 blem.\nThis is joint work with M. Bertola and A. Katsevich\, accepted in P
 roceedings of the AMS
LOCATION:MR 14\, CMS
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