Banach spaces related to integrable group representations and their atomic decompositions, I

Wilson Bases and Ultramodulation Spaces

“…fulfills the conditions of the general theory exposed in [FG1]. From the general theory of coorbit spaces it follows that the Proposition 4.3 holds true.…”

“…[F1], [F2], [FG1]). In the next proposition we show that the space M w1⊗1 2,2 is also a Wiener amalgam space.…”

“…These spaces are the most important examples of coorbit spaces analyzed in the celebrated papers [FG1] and [FG2]. Almost all classical function spaces appear naturally as coorbits of certain integrable representations (cf.…”

Separability criteria via wavelet transform on homogenous spaces and projective representations

“…We only mention the concepts that will be needed in the sequel, a more detailed treatment may be found in 1 [22][23][24], for example. Let G be a locally compact group with the left Haar measure µ and H be a closed subgroup of G. Letπ be a continuous representation of a group and X = G/H a homogeneous space.…”

Homogeneous approximation property for wavelet frames with matrix dilations

“…Similar to the Feichtinger's algebra S 0 studied in [11,13] for Gabor analysis, F 1 (R d ) contains nice wavelet atoms and therefore are useful in wavelet analysis. For example, functions from F 1 (R d ) generate wavelet frames for every well-spread time-scale sequences of the form {(s j , s j t k ) : j, k ∈ Z}.…”