Wiener amalgam space

In mathematics, amalgam spaces categorize functions with regard to their local and global behavior. While the concept of function spaces treating local and global behavior separately was already known earlier, Wiener amalgams, as the term is used today, were introduced by Hans Georg Feichtinger in 1980. The concept is named after Norbert Wiener.
Let formula_1 be a normed space with norm formula_2. Then the "Wiener amalgam space" with local component formula_1 and
global component formula_4, a weighted formula_5 space with non-negative weight formula_6, is defined by
where formula_8 is a continuously differentiable, compactly supported function, such that formula_9, for all formula_10. Again, the space defined is independent of formula_8. As the definition suggests, Wiener amalgams are useful to describe functions showing characteristic local and global behavior.