Deformation quantization and Borel's theorem in locally convex spaces

• Autorzy: Miroslav Engliš , Jari Taskinen
• Języki publikacji: EN

Abstrakty

EN

It is well known that one can often construct a star-product by expanding the product of two Toeplitz operators asymptotically into a series of other Toeplitz operators multiplied by increasing powers of the Planck constant h. This is the Berezin-Toeplitz quantization. We show that one can obtain in a similar way in fact any star-product which is equivalent to the Berezin-Toeplitz star-product, by using instead of Toeplitz operators other suitable mappings from compactly supported smooth functions to bounded linear operators on the corresponding Hilbert spaces. A crucial ingredient in the proof is the generalization, due to Colombeau, of the classical theorem of Borel on the existence of a function with prescribed derivatives of all orders at a point, which reduces the proof to a construction of a locally convex space enjoying some special properties.

Kategorie tematyczne

• 26B05: Continuity and differentiation questions
• 53D55: Deformation quantization, star products
• 46A13: Spaces defined by inductive or projective limits (LB, LF, etc.)
• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 180
• Numer: 1
• Strony: 77-93

Daty

wydano

2007

Twórcy

autor

Miroslav Engliš

• Mathematics Institute, Žitná 25, 11567 Praha 1, Czech Republic
• Mathematics Institute, Na Rybníčku 1, 74601 Opava, Czech Republic

autor

Jari Taskinen

• Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FIN-00014 Helsinki, Finland

Identyfikatory

DOI

10.4064/sm180-1-6