The classical limit in weyl quantization

Antonets, M. A.

doi:10.1007/bf01077563

Cited by 9 publications

(14 citation statements)

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“…In particular, one gets naturally an optimal multiplier-type algebra that we call the Moyal algebra. Such an object has been studied in connection with the Weyl pseudodifferential calculus [1,8,9], starting with the natural algebraico-topological structure of the Schwartz space S(R n ). An adaptation for the Gelfand-Shilov spaces is contained in [22] .…”

Section: Introductionmentioning

confidence: 99%

On Fréchet–Hilbert algebras

Măntoiu

Purice

2014

Arch. Math.

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We consider Hilbert algebras with a supplementary Fréchet topology and get various extensions of the algebraic structure by using duality techniques. In particular we obtain optimal multiplier-type involutive algebras, which in applications are large enough to be of significant practical use. The setting covers many situations arising from quantization rules, as those involving square-integrable families of bounded operators Address

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Section: Introductionmentioning

confidence: 99%

On Fréchet–Hilbert algebras

Măntoiu

Purice

2014

Arch. Math.

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“…But in practice, depending on the problem under study, we must consider an extension of these operations to one or another subspace of the dual space S ′ of tempered distributions. Antonets proposed a maximal extension by duality that consisted in constructing the multiplier algebra of the algebra (S, ⋆ θ ) [4]- [6] or, equivalently, of the algebra (S, ⊛ θ ). This extension was later studied in many papers and most thoroughly in [7]- [10] (a detailed review and references can be found in [11]).…”

Section: Introductionmentioning

confidence: 99%

Twisted convolution and Moyal star product of generalized functions

Soloviev

2012

Theor Math Phys

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Abstract. We consider nuclear function spaces on which the Weyl-Heisenberg group acts continuously and study the basic properties of the twisted convolution product of the functions with the dual space elements. The final theorem characterizes the corresponding algebra of convolution multipliers and shows that it contains all sufficiently rapidly decreasing functionals in the dual space. Consequently, we obtain a general description of the Moyal multiplier algebra of the Fourier-transformed space. The results extend the Weyl symbol calculus beyond the traditional framework of tempered distributions.

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“…Various classes of distributions were considered. For example, Antonets, [2], considered the * -algebra W of * -multipliers of the test functions (we shall denote this space as N ∩ N in this paper). These are the distributions whose Weyl quantizations are (continuous) endomorphisms of Schwartz space with adjoints which are also such endomorphisms.…”

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confidence: 99%