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DC Field | Value | Language |
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dc.contributor.author | Zheleznyak, Alexandr V. | - |
dc.date.accessioned | 2021-05-04T19:05:41Z | - |
dc.date.available | 2021-05-04T19:05:41Z | - |
dc.date.issued | 2021-03 | - |
dc.identifier.citation | Zheleznyak А.V. Power series of several variables with condition of logarithmical convexity. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 1, pp. 49–62. | en_GB |
dc.identifier.other | https://doi.org/10.21638/spbu01.2021.105 | - |
dc.identifier.uri | http://hdl.handle.net/11701/28433 | - |
dc.description.abstract | We obtain a new version of Hardy theorem about power series of several variables reciprocal to the power series with positive coefficients. We prove that if the sequence {as} = as1,s2,...,sn, ||s|| ≥ K satisfies condition of logarithmically convexity and the first coefficient a0 is sufficiently large then reciprocal power series has only negative coefficients {bs} = bs1,s2,...,sn, except b0,0,...,0 for any K. The classical Hardy theorem corresponds to the case K = 0, n = 1. Such results are useful in Nevanlinna - Pick theory. For example, if function k(x, y) can be represented as power series Pn≥0 an(x¯y)n, an > 0, and reciprocal function 1 k(x,y) can be represented as power series Pn≥0 bn(x¯y)n such that bn < 0, n > 0, then k(x, y) is a reproducing kernel function for some Hilbert space of analytic functions in the unit disc D with Nevanlinna-Pick property. The reproducing kernel 1 1−x¯y of the classical Hardy space H2(D) is a prime example for our theorems. | en_GB |
dc.language.iso | ru | en_GB |
dc.publisher | St Petersburg State University | en_GB |
dc.relation.ispartofseries | Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 8 (66); Issue 1 | - |
dc.subject | power series | en_GB |
dc.subject | Nevanlinna - Pick kernels | en_GB |
dc.subject | logarithmical convexity | en_GB |
dc.title | Power series of several variables with condition of logarithmical convexity | en_GB |
dc.type | Article | en_GB |
Appears in Collections: | Issue 1 |
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