Abstract: 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

Publication: Nature Vol.: 350 No.: 6318 ISSN: 0028-0836

ID: CaltechAUTHORS:20150514-144638393

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Abstract: 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].

Publication: Pacific Journal of Mathematics Vol.: 47 No.: 2 ISSN: 0030-8730

ID: CaltechAUTHORS:BENpjm73

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