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Segal–Bargmann and Weyl transforms on compact Lie groups. (With Joachim Hilgert)

Författare och institution:
J. Hilgert (-); Genkai Zhang (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Publicerad i:
Monatshefte für Mathematik , 158 ( 3 ) s. 285-305
ISSN:
0026-9255
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2009
Språk:
engelska
Fulltextlänk:
Sammanfattning (abstract):
We present an elementary derivation of the reproducing kernel for invariant Fock spaces associated with compact Lie groups which, as Ólafsson and Ørsted showed in (Lie Theory and its Applicaitons in Physics. World Scientific, 1996), yields a simple proof of the unitarity of Hall's Segal-Bargmann transform for compact Lie groups K. Further, we prove certain Hermite and character expansions for the heat and reproducing kernels on K and Kℂ. Finally, we introduce a Toeplitz (or Wick) calculus as an attempt to have a quantization of the functions on Kℂ as operators on the Hilbert space L2(K).
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik
Nyckelord:
Compact lie group; Hermite functions; Reproducing kernel; Segal-Bargmann transform; Toeplitz operator; Weyl transform
Postens nummer:
102830
Posten skapad:
2009-12-04 15:11
Posten ändrad:
2016-07-12 15:47

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