University of Cambridge > > Applied and Computational Analysis > Inversion formulae for the cosh-weighted Hilbert transform

Inversion formulae for the cosh-weighted Hilbert transform

Add to your list(s) Download to your calendar using vCal

  • UserAlexander Tovbis (Dep. of Mathematics University of Central Florida)
  • ClockThursday 06 December 2012, 15:00-16:00
  • HouseMR 14, CMS.

If you have a question about this talk, please contact Carola-Bibiane Schoenlieb.

This talk has been canceled/deleted

We develop formulae for inverting the so-called cosh-weighted Hilbert transform H_μ, which arises in Single Photon Emission Computed Tomography (SPECT). The formulae are theoretically exact, require the minimal 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-space 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 trivial 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 the case p = 2 we find the range condition for H_μ, which is similar to that for the FHT H _0. Our work is based on the method of Riemann-Hilbert problem. This is joint work with M. Bertola and A. Katsevich, accepted in Proceedings of the AMS

This talk is part of the Applied and Computational Analysis series.

Tell a friend about this talk:

This talk is included in these lists:

This talk is not included in any other list

Note that ex-directory lists are not shown.


© 2006-2024, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity