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Issue ESAIM: Proc.
Volume 26, 2009
Mathematical methods for imaging and inverse problems
Page(s) 55 - 64
DOI http://dx.doi.org/10.1051/proc/2009005
Published online 25 April 2009

ESAIM: Proc., 2009, Vol. 26, pp. 55-64
DOI: 10.1051/proc/2009005

Generalized Fourier Transforms, Inverse Problems, and Integrability in 4+2

A.S. Fokas

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK


Published online: 25 April 2009

Abstract
Three different types of generalized Fourier transforms are discussed, which appear in the following: (a) The medical imaging technique called Single Photon Emission Computerized Tomography (SPECT). (b) The solution of the Cauchy problem of integrable nonlinear evolution PDEs in 4+2, i.e. in four spatial and two temporal dimensions. (c) The characterization of the generalized Dirichlet to Neumann map for integrable nonlinear evolution PDEs in 1+1, i.e. in one spatial and one temporal dimensions.


Mathematics Subject Classification. 35R30

Key words: Generalized Fourier transforms, generalized Dirichlet to Neumann map, integrable nonlinear evolution PDEs, Single Photon Emission Computerized Tomography.


© EDP Sciences, ESAIM 2009


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