Quantization Rules, Hilbert Algebras and Coorbit Spaces for Families of Bounded Operators I. The Abstract Theory

Details Quantization Rules, Hilbert Algebras and Coorbit Spaces for Families of Bounded Operators I. The Abstract Theory Quantization Rules, Hilbert Algebras and Coorbit Spaces for Families of Bounded Operators I. The Abstract Theory

2012-03-28

arxiv.org/abs/1203.6347v1

Mathematics

Functional Analysis

31 pages

Scientific paper

The starting point is a continuous family of bounded operators in a Hilbert space, indexed by a locally compact space. A certain square integrability condition is required with respect to a given Radon measure. Then one constructs and studies a symbolic calculus, various Gelfand triples with nice algebraic properties as well as coorbit spaces of vectors and symbols.The aim is to unify within the coorbit theory recent global pseudodifferential theories going beyond the group theoretic point of view.

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