The Feichtinger Algebra
We are now going to address a first topic from the theory of modulation spaces, which was initiated by Feichtinger in the early 1980’s: the Feichtinger algebra S 0(ℝ n ) (we will study the general notion of modulation space in the next chapter). The elements of S 0(ℝ n ) are characterized by the property that their Wigner transform is in L 1(ℝ n ⊕ ℝ n ), but it is not obvious at all that, with this definition, S 0(ℝ n ) is a vector space, even less an algebra! We will therefore need an alternative, more tractable, equivalent definition.
KeywordsBanach Algebra Inversion Formula Modulation Space Gabor Frame Weyl Operator
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