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Izv. RAN. Ser. Mat., 2004, Volume 68, Issue 5, Pages 189–212 (Mi izv507)  

On the completeness of sparse subsequences of systems of functions of the form $f^{(n)}(\lambda_nz)$

A. Yu. Popov


Abstract: We obtain some new results on the completeness of systems of functions $f^{(n)}(\lambda_nz)$ in the space of entire functions with the topology of uniform convergence on an arbitrary compact set in $\mathbb C$. In the presence of lacunae in the Taylor expansion of the function $f(z)$, we prove the existence of bases consisting of subsystems of this form.

DOI: https://doi.org/10.4213/im507

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English version:
Izvestiya: Mathematics, 2004, 68:5, 1025–1049

Bibliographic databases:

UDC: 517.538.2
MSC: 30B60, 30D10, 30D15, 30D35, 46E10
Received: 25.11.2003

Citation: A. Yu. Popov, “On the completeness of sparse subsequences of systems of functions of the form $f^{(n)}(\lambda_nz)$”, Izv. RAN. Ser. Mat., 68:5 (2004), 189–212; Izv. Math., 68:5 (2004), 1025–1049

Citation in format AMSBIB
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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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