R. S. Ismagilov, K. V. Uskov, “Asymptotics of the <nobr>$n$</nobr>-Widths of a Wiener Spiral in Complex Hilbert Space”, Mat. Zametki, 2011, Volume 89, Issue 5,Pages <nobr>686

Asymptotics of the $n$-Widths of a Wiener Spiral in Complex Hilbert Space

R. S. Ismagilov^a, K. V. Uskov^b

^a N. E. Bauman Moscow State Technical University
^b OAO "Gasprombank"

Abstract: We describe isometric embeddings of the Wiener spiral in complex Hilbert space and obtain the asymptotics of the Kolmogorov $n$-widths of specific embeddings. We note the difference with the asymptotics of the $n$-widths of the Wiener spiral in real Hilbert space.

Keywords: Wiener spiral, Kolmogorov $n$-width, complex Hilbert space, real Hilbert space, isometric embedding, correlation function of a mapping, Hermitian kernel.

UDC: 517.518.224

Received: 18.11.2010

DOI: 10.4213/mzm9120