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Vector valued Fourier analysis on unimodular groups
Author(s) -
Lee Hun Hee
Publication year - 2006
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310399
Subject(s) - unimodular matrix , mathematics , abelian group , fourier transform , heisenberg group , pure mathematics , fourier inversion theorem , type (biology) , group (periodic table) , banach space , fourier analysis , mathematical analysis , fractional fourier transform , physics , ecology , quantum mechanics , biology
The notion of Fourier type and cotype of linear maps between operator spaces with respect to certain unimodular (possibly nonabelian and noncompact) group is defined here. We develop analogous theory compared to Fourier types with respect to locally compact abelian groups of operators between Banach spaces. We consider the Heisenberg group as an example of nonabelian and noncompact groups and prove that Fourier type and cotype with respect to the Heisenberg group implies Fourier type with respect to classical abelian groups. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)