English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We give a constructive proof of the finite version of Gowers' $FIN_k$ Theoremand analyse the corresponding upper bounds. The $FIN_k$ Theorem is closelyrelated to the oscillation stability of $c_0$. The stabilization of Lipschitzfunctions on arbitrary finite dimensional Banach spaces was studied well beforeby V. Milman. We compare the finite $FIN_k$ Theorem with the finitestabilization principle in the case of spaces of the form $\ell_{\infty}^n$,$n\in\mathbb{N}$ and establish a much slower growing upper bound for the finitestabilization principle in this particular case.

Finite forms of Gowers' Theorem on the oscillation stability of $c_0$