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.
متن کاملSpectral results for operators commuting with translations on Banach spaces of sequences on Zk and Z+
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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The theory of commuting linear differential expressions has received a lot of attention since Lax presented his description of the KdV hierarchy by Lax pairs (P,L). Gesztesy and the present author have established a relationship of this circle of ideas with the property that all solutions of the differential equations Ly = zy, z ∈ C, are meromorphic. In this paper this relationship is explored ...
متن کاملEssentially Commuting Toeplitz Operators
For f in L∞, the space of essentially bounded Lebesgue measurable functions on the unit circle, ∂D, the Toeplitz operator with symbol f is the operator Tf on the Hardy space H2 of the unit circle defined by Tfh = P (fh). Here P denotes the orthogonal projection in L2 with range H2. There are many fascinating problems about Toeplitz operators ([3], [6], [7] and [20]). In this paper we shall conc...
متن کاملCommuting aggregation operators
We will investigate so-called commuting operators and their relationship to bisymmetry and domination. In the case of bisymmetric aggregation operators we will show a sufficient condition ensuring that two operators commute, while for bisymmetric aggregation operators with neutral element we will even give a full characterization of commuting n-ary operators by means of unary commuting operators.
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1966
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1966.16.259