On a (No Longer) New Segal Algebra: A Review of the Feichtinger Algebra

• Published in: The Journal of fourier analysis and applications Vol. 24; no. 6; pp. 1579 - 1660
• Main Author: Jakobsen, Mads S.
• Format: Journal Article
• Language: English
• Published: New York Springer US 15.12.2018; Springer; Springer Nature B.V
• Subjects: Abstract Harmonic Analysis; Algebra; Analysis; Approximations and Expansions; Banach spaces; Differential equations; Fourier Analysis; Function space; Isomorphism; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Operators (mathematics); Partial Differential Equations; Signal,Image and Speech Processing; Theorems; Time-frequency analysis; Schwartz–Bruhat space; Secondary 43-02; Feichtinger algebra; Generalized functions; Test functions; Primary 43A15

Since its invention in 1979 the Feichtinger algebra has become a useful Banach space of functions with applications in time-frequency analysis, the theory of pseudo-differential operators and several other topics. It is easily defined on locally compact Abelian groups and, in comparison with the Sch...