This chapter is concerned with recent progress in the context of coorbit space theory. Based on a square-integrable group representation, the coorbit theory provides new families of associated smoothness spaces, where the smoothness of a function is measured by the decay of the associated voice transform. Moreover, by discretizing the representation, atomic decompositions and Banach frames can be constructed. Usually, the whole machinery works well if the associated reproducing kernel is integrable with respect to a weighted Haar measure on the group. In recent studies, it has turned out that to some extent coorbit spaces can still be established if this condition is violated. In this chapter, we clarify in which sense atomic decompositions and Banach frames for these generalized coorbit spaces can be obtained.
On the atomic decomposition of coorbit spaces with non-integrable kernel
De Mari F.;De Vito E.;
2019-01-01
Abstract
This chapter is concerned with recent progress in the context of coorbit space theory. Based on a square-integrable group representation, the coorbit theory provides new families of associated smoothness spaces, where the smoothness of a function is measured by the decay of the associated voice transform. Moreover, by discretizing the representation, atomic decompositions and Banach frames can be constructed. Usually, the whole machinery works well if the associated reproducing kernel is integrable with respect to a weighted Haar measure on the group. In recent studies, it has turned out that to some extent coorbit spaces can still be established if this condition is violated. In this chapter, we clarify in which sense atomic decompositions and Banach frames for these generalized coorbit spaces can be obtained.File | Dimensione | Formato | |
---|---|---|---|
ON THE ATOMIC DECOMPOSITION OF COORBIT SPACESWITH NON-INTEGRABLE KERNEL.pdf
accesso aperto
Tipologia:
Documento in Pre-print
Dimensione
622.1 kB
Formato
Adobe PDF
|
622.1 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.