Dual pairs of sequence spaces. III

Coorbit Spaces for Dual Pairs

In this paper we present an abstract framework for construction of Banach spaces of distributions from group representations. This generalizes the theory of coorbit spaces initiated by H.G. Feichtinger and K. Gröchenig in the 1980’s. Spaces that can be described by this new technique include the whole Banach-scale of Bergman spaces on the unit disc. For these Bergman spaces we show that atomic ...

Examples of Coorbit Spaces for Dual Pairs

In this paper we summarize and give examples of a generalization of the coorbit space theory initiated in the 1980’s by H.G. Feichtinger and K.H. Gröchenig. Coorbit theory has been a powerful tool in characterizing Banach spaces of distributions with the use of integrable representations of locally compact groups. Examples are a wavelet characterization of the Besov spaces and a characterizatio...

Complementary Sequence Pairs of Types II and III

We refer to this conventional type of complementary pair as a Type-I pair and, in this paper, investigate two variants of the complementary pair, namely TypeII and Type-III complementary pairs. Type-I complementary pairs are attractive because the sum of their aperiodic autocorrelations, λAB , has zero sidelobes, i.e. λAB(z) has no dependence on z. This means that the Fourier transform of λAB i...

Reciprocal maximum-length sequence pairs for acoustical dual source measurements.

In this paper we propose and demonstrate a method to obtain simultaneous dual source-receiver impulse responses in acoustical systems using binary maximum-length sequences (MLS). A binary MLS and its reversed-order sequence form a reciprocal MLS pair. Their correlation property includes a two-valued "pulse-like" autocorrelation function and a relatively smaller-valued cross-correlation function...

A New Class of Banach Sequence Spaces