HR: 10:25h
AN: IN22A-01    [Abstracts]
TI: Time and band limitation of tensor-valued functions
AU: * Grunbaum, A
EM: albertogrunbaum@yahoo.com
AF: University of California Berkeley, Mathematics Department 903 Evans Hall, Berkeley, CA 94720-3840
AB: The problem of making optimal use of "low frequency data" for a function on the sphere which is either supported in a spherical cap, or for which one is mainly interested on its values on such a cap, gives rise to an extension of the remarkable work of Slepian, Landau and Pollak (Bell Labs, 1960). This issue was addressed back around 1980 in the case when the groups involved are the rotation groups in dimension two and three and provides an extension of the classical work started by Claude Shannon in the context of communication theory where the group is the real line. Considerations along these lines have appeared more recently in the geophysical context, such as in the work of Albertella, Sanso and Sneeuw or in work of Simons, Dahlen and Wieczorek. Very recently I have considered the problem of reconstructing "tensor or matrix valued quantities" once again using mainly low frequency data. Mathematically this leads to taking a new look at the work from the 1980's replacing the orthogonal groups in question by unitary groups. The mathematics is now much harder, due to the tensorial character of the quantities in question. I am extremely interested in finding good geophysical applications of these recent developments.
DE: 3200 MATHEMATICAL GEOPHYSICS (0500, 4400, 7833)
DE: 3205 Fourier analysis (3255)
SC: Earth and Space Science Informatics [IN]
MN: Fall Meeting 2005