Semigroups of operators commuting with translations
نویسندگان
چکیده
منابع مشابه
Operators Commuting with a Discrete Subgroup of Translations
We study the structure of operators from the Schwartz space S (R) into the tempered distributions S (R) that commute with a discrete subgroup of translations. The formalism leads to simple derivations of recent results about the frame operator of shift-invariant systems, Gabor and wavelet frames.
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We study the spectrum of multipliers (bounded operators commuting with the shift operator S) on a Banach space E of sequences on Z. Given a multiplier M , we prove that f M(σ(S)) ⊂ σ(M) where f M is the symbol of M . We obtain a similar result for the spectrum of an operator commuting with the shift on a Banach space of sequences on Z. We generalize the results for multipliers on Banach spaces ...
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It is known that ring and semigroup theories have evolved many similar methods. The exchange of ideas between these theories has enriched both of them. Among ring concepts transfered to semigroups, the notion of a radical deserves mentioning. The analogy with radicals of rings suggests that semigroup radicals may be applicable in studying the structure of semigroups. On the other hand, many str...
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Let S1 = {Ft}t≥0 and S2 = {Gt}t≥0 be two continuous semigroups of holomorphic self-mappings of the unit disk ∆ = {z : |z| < 1} generated by f and g, respectively. We present conditions on the behavior of f (or g) in a neighborhood of a fixed point of S1 (or S2), under which the commutativity of two elements, say, F1 and G1 of the semigroups implies that the semigroups commute, i.e., Ft◦Gs = Gs◦...
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Certain criteria are demonstrated for a spatial derivation of a von Neumann algebra to generate a one-parameter semigroup of endomorphisms of that algebra. These are then used to establish a converse to recent results of Borchers and of Wiesbrock on certain one-parameter semigroups of endomorphisms of von Neumann algebras (specifically, Type III1 factors) that appear as lightlike translations i...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1974
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-31-2-253-258