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On homogeneous decomposition spaces and associated decompositions of distribution spaces
Author(s) -
AlJawahri Zeineb,
Nielsen Morten
Publication year - 2019
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.201700474
Subject(s) - mathematics , smoothness , homogeneous , modulo , pure mathematics , norm (philosophy) , decomposition , simple (philosophy) , mathematical analysis , discrete mathematics , combinatorics , ecology , biology , philosophy , epistemology , political science , law
A new construction of decomposition smoothness spaces of homogeneous type is considered. The smoothness spaces are based on structured and flexible decompositions of the frequency spaceR d ∖ { 0 }. We construct simple adapted tight frames forL 2 ( R d ) that can be used to fully characterise the smoothness norm in terms of a sparseness condition imposed on the frame coefficients. Moreover, it is proved that the frames provide a universal decomposition of tempered distributions with convergence in the tempered distributions modulo polynomials. As an application of the general theory, the notion of homogeneous α‐modulation spaces is introduced.