CaltechAUTHORS: Combined
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenMon, 11 Nov 2024 06:52:17 -0800A Hausdorff-Young theorem for rearrangement-invariant spaces
https://resolver.caltech.edu/CaltechAUTHORS:BENpjm73
Year: 1973
The classical Hausdorff-Young theorem is extended to the setting of rearrangement-invariant spaces. More precisely, if 1 <_ p <_ 2, p[-1] + q[-1] = 1, and if X is a rearrangement-invariant space on the circle T with indices equal to p[-1], it is shown that there is a rearrangement-invariant space X on the integers Z with indices equal to q[-1] such that the Fourier transform is a bounded linear operator from X into X. Conversely, for any rearrangement-invariant space Y on Z with indices equal to q[-1], 2 < q <__ oo, there is a rearrangement-invariant space Y on T with indices equal to p[-1] such that J is bounded from Y into Y. Analogous results for other groups are indicated and examples are discussed when X is L[p] or a Lorentz space L[pr].https://resolver.caltech.edu/CaltechAUTHORS:BENpjm73'Life' not critical?
https://resolver.caltech.edu/CaltechAUTHORS:20150514-144638393
Year: 1991
DOI: 10.1038/350468a0
SIR - Bak et al. have presented evidence that the cellular automaton, the 'game of life', develops into a self-organized critical state, characterized by a D(T)^(-1.6) distribution of times T required for the lattice to return to equilibrium following a random
single-site perturbation. This power law implies an infinite expected equilibration time .https://resolver.caltech.edu/CaltechAUTHORS:20150514-144638393