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Anti-Wick quantization with symbols in $L^p$ spaces


Authors: Paolo Boggiatto and Elena Cordero
Journal: Proc. Amer. Math. Soc. 130 (2002), 2679-2685
MSC (2000): Primary 47G30, 35S05
DOI: https://doi.org/10.1090/S0002-9939-02-06348-7
Published electronically: February 4, 2002
MathSciNet review: 1900876
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Abstract: We give a classification of pseudo-differential operators with anti-Wick symbols belonging to $L^p$ spaces: if $p=1$ the corresponding operator belongs to trace classes; if $1\leq p\leq 2$ we get Hilbert-Schmidt operators; finally, if $p<\infty$, the operator is compact. This classification cannot be improved, as shown by some examples.


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Additional Information

Paolo Boggiatto
Affiliation: Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
Email: boggiatto@dm.unito.it

Elena Cordero
Affiliation: Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
Email: cordero@dm.unito.it

DOI: https://doi.org/10.1090/S0002-9939-02-06348-7
Keywords: Anti-Wick, pseudo-differential operators, Hilbert-Schmidt, trace class
Received by editor(s): April 12, 2001
Published electronically: February 4, 2002
Communicated by: David Tartakoff
Article copyright: © Copyright 2002 American Mathematical Society

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