COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

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

## Inversion formulae for the cosh-weighted Hilbert transformAdd to your list(s) Download to your calendar using vCal - Alexander Tovbis (Dep. of Mathematics University of Central Florida)
- Thursday 06 December 2012, 15:00-16:00
- MR 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. ## This talk is included in these lists:This talk is not included in any other list Note that ex-directory lists are not shown. |
## Other listsResearch Seminars - Department of Biochemistry 2008/09 Type the title of a new list here Interfacial Studies on a Charged Surface in Oil by Contact Angle Measurements Workshop on Epigenetics in Gastrointestinal Health and Disease BCNI seminars EDC Inclusive design## Other talks'Ways of Reading, Looking, and Imagining: Contemporary Fiction and Its Optics' Beating your final boss battle, or presenting with confidence and style (easy mode) Reserved for CambPlants Connecting behavioural and neural levels of analysis MEASUREMENT SYSTEMS AND INSTRUMENTATION IN THE OIL AND GAS INDUSTRY Metamaterials and the Science of Invisibility From Euler to Poincare Towards a whole brain model of perceptual learning Genomic Approaches to Cancer A polyfold lab report Picturing the Heart in 2020 Finding the past: Medieval Coin Finds at the Fitzwilliam Museum |