Geodesic
Asymptotics of the $n$-Widths of a Wiener Spiral in Complex Hilbert Space
Matematičeskie zametki, Tome 89 (2011) no. 5, pp. 686-693 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {R. S. Ismagilov and K. V. Uskov},
     title = {Asymptotics of the $n${-Widths} of a {Wiener} {Spiral} in {Complex} {Hilbert} {Space}},
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R. S. Ismagilov; K. V. Uskov. Asymptotics of the $n$-Widths of a Wiener Spiral in Complex Hilbert Space. Matematičeskie zametki, Tome 89 (2011) no. 5, pp. 686-693. http://geodesic.mathdoc.fr/item/MZM_2011_89_5_a4/

[1] A. Kolmogoroff, “Über die beste Annäherung von Funktionen einer gegebenen Funktionenklasse”, Ann. of Math. (2), 37:1 (1936), 107–110 | MR | Zbl

[2] V. M. Tikhomirov, Nekotorye voprosy teorii priblizhenii, Izd-vo Mosk. un-ta, M., 1976 | MR

[3] A. N. Kolmogorov, A. A. Petrov, Yu. M. Smirnov, “Odna formula Gaussa iz teorii metoda naimenshikh kvadratov”, Izv. AN SSSR. Ser. matem., 11:6 (1947), 561–566 | MR | Zbl

[4] “Ob $n$-mernykh poperechnikakh kompaktov v gilbertovom prostranstve”, Funkts. analiz i ego pril., 2:2 (1968), 32–39 | MR | Zbl

[5] K. V. Uskov, “O nakhozhdenii tochnogo znacheniya kolmogorovskikh poperechnikov kompakta v gilbertovom prostranstve”, Matem. zametki, 72:4 (2002), 570–586 | MR | Zbl