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Morrey sequence spaces

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ASC - Approximation, sampling and compression in data science

Morrey (function) spaces and, in particular, smoothness spaces of Besov-Morrey or Triebel-Lizorkin-Morrey type were studied in recent years quite intensively and systematically. Decomposition methods like atomic or wavelet characterisations require suitably adapted sequence spaces. This has been done to some extent already. However, based on some discussion at a conference in Poznan in 2017 we found that Morrey sequence spaces $m_{u,p}=m_{u,p}(\mathbb{Z}^d)$, $0 We consider some basic features, embedding properties, a pre-dual, a corresponding version of Pitt's compactness theorem, and can further characterise the compactness of embeddings of related finite dimensional spaces in terms of their entropy numbers.
This is joint work with Leszek Skrzypczak (Poznan).

This talk is part of the Isaac Newton Institute Seminar Series series.

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