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Ufimsk. Mat. Zh., 2017, Volume 9, Issue 3, Pages 102–110 (Mi ufa389)  

Invariant subspaces with zero density spectrum

O. A. Krivosheeva

Bashkir State University, Zaki Validi str. 32, 450076, Ufa, Russia

Abstract: In the paper we show that each analytic solution of a homogeneous convolution equation with the characteristic function of minimal exponential type is represented by a series of exponential polynomials in its domain. This series converges absolutely and uniformly on compact subsets in this domain. It is known that if the characteristic function is of minimal exponential type, the density of its zero set is equal to zero. This is why in the work we consider the sequences of exponents having zero density. We provide a simple description of the space of the coefficients for the aforementioned series. Moreover, we provide a complete description of all possible system of functions constructed by rather small groups, for which the representation by the series of exponential polynomials holds.

Keywords: A series of exponential monomials, relatively small clusters, basis, convex domain.

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English version:
Ufa Mathematical Journal, 2017, 9:3, 100–108 (PDF, 325 kB); https://doi.org/10.13108/2017-9-3-100

Bibliographic databases:

UDC: 517.5
MSC: 30D10
Received: 31.10.2016

Citation: O. A. Krivosheeva, “Invariant subspaces with zero density spectrum”, Ufimsk. Mat. Zh., 9:3 (2017), 102–110; Ufa Math. J., 9:3 (2017), 100–108

Citation in format AMSBIB
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