[
{
"id": "authors:r72sa-nrc86",
"collection": "authors",
"collection_id": "r72sa-nrc86",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150514-144638393",
"type": "article",
"title": "'Life' not critical?",
"author": [
{
"family_name": "Bennett",
"given_name": "Charles",
"clpid": "Bennett-C"
},
{
"family_name": "Bourzutschky",
"given_name": "Mark S.",
"clpid": "Bourzutschky-M-S"
}
],
"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\nsingle-site perturbation. This power law implies an infinite expected equilibration time .",
"doi": "10.1038/350468a0",
"issn": "0028-0836",
"publisher": "Nature Publishing Group",
"publication": "Nature",
"publication_date": "1991-04-11",
"series_number": "6318",
"volume": "350",
"issue": "6318",
"pages": "468"
},
{
"id": "authors:vt99t-31f54",
"collection": "authors",
"collection_id": "vt99t-31f54",
"cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:BENpjm73",
"type": "article",
"title": "A Hausdorff-Young theorem for rearrangement-invariant spaces",
"author": [
{
"family_name": "Bennett",
"given_name": "Colin",
"clpid": "Bennett-C"
}
],
"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].",
"issn": "0030-8730",
"publisher": "Pacific Journal of Mathematics",
"publication": "Pacific Journal of Mathematics",
"publication_date": "1973",
"series_number": "2",
"volume": "47",
"issue": "2",
"pages": "311-328"
}
]