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Wilson Bases and Modulation Spaces
Author(s) -
Feichtinger H. G.,
Gröchenig K.,
Walnut D.
Publication year - 1992
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.19921550102
Subject(s) - mathematics , modulation space , pure mathematics , space (punctuation) , algebra over a field , exponential function , basis (linear algebra) , mathematical analysis , geometry , philosophy , linguistics
We show that the recently discovered W ILSON bases of exponential decay are unconditional bases for all modulation spaces on R , including the classical B ESSEL potential spaces, the Segal algebra S o , and the S CHWARTZ space. As a consequence we obtain new bases for spaces of entire functions. On the other hand, the W ILSON bases are no unconditional bases for the ordinary L p ‐spaces for p ≠ 2.