caa a22 4500 463246845 CHVBK 20180405153328.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s00041-006-6009-x doi (NATIONALLICENCE)springer-10.1007/s00041-006-6009-x Engliš Miroslav Mathematics Institute, Žitná 25, 11567 Prague 1, Czech Republic and Mathematics Institute, Silesian University at Opava, Na Rybnícku 1, 74601 Opava, Czech Republic aut Toeplitz Operators and Group Representations [Elektronische Daten] [Miroslav Engliš] Toeplitz operators on the Bergman space of the unit disc can be written as integrals of the symbol against an invariant operator field of rank-one projections. We consider a generalization of the Toeplitz calculus obtained upon taking more general invariant operator fields, and also allowing more general domains than the disc; such calculi were recently introduced and studied by Arazy and Upmeier, but also turn up as localization operators in time-frequency analysis (witnessed by recent articles by Wong and others) and in representation theory and mathematical physics. In particular, we establish basic properties like boundedness or Schatten class membership of the resulting operators. A further generalization to the setting when there is no group action present is also discussed, and the various settings in which similar operator calculi appear are briefly surveyed. Birkhauser Boston, 2007 Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/3(2007-06-01), 243-265 1069-5869 13:3<243 2007 13 41 https://doi.org/10.1007/s00041-006-6009-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00041-006-6009-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Engliš Miroslav Mathematics Institute, Žitná 25, 11567 Prague 1, Czech Republic and Mathematics Institute, Silesian University at Opava, Na Rybnícku 1, 74601 Opava, Czech Republic aut NATIONALLICENCE 773 0- Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/3(2007-06-01), 243-265 1069-5869 13:3<243 2007 13 41 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer