Amalgam spaces and generalized harmonic analysis
Hans Georg Feichtinger · Proceedings of symposia in applied mathematics · 1995
It is the purpose of this short note to indicate in which way certain amalgam spaces, defined in the spirit of N. Wiener, can be used to deal with questions arising in generalized harmonic analysis in several dimensions. In some sense these results are natural extensions of corresponding onedimensional results due to N. Wiener (e.g. Theorem 29 in his book [33i]). Amalgams are taken with respect to "dyadic" and "uniform" decompositions respectively. 1 Introduction In this short note we collect several interesting mathematical results, involving certain function spaces with mixed norms, which in certain special cases have been used in N. Wiener's work. Essentially, we cover the following three topics: ffl Tauberian Theorems (Wiener's Third theorem) in higher dimensions ffl A new generalization (even for IR d ) of Wiener's algebra A(II ) to locally compact Abelian groups ffl Some comments on Gabor analysis 2 Tauberian Theorems in higher dimensions Wiener's Theory of Tauberian Theo...