INTERPOLATION FOR P-ADIC ENTIRE FUNCTIONS
2010 ◽
Vol 03
(02)
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pp. 251-262
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Let K be a complete ultrametric algebraically closed field. This paper is aimed at studying problems of interpolation for entire functions on K. We prove an analogue of M . Lazard's divisors theorem for entire functions and then we show that sequences of interpolation are the injective sequences (ai)i∈ N in K such that lim i→∞ |ai| = +∞. This result does not assume K to be spherically complete. In order to construct concrete entire interpolation functions, we introduce Lagrange entire functions and define L-sequences. We show that a sequence (ai)i∈ N in K defines a Lagrange entire function if and only if (ai)i∈ N is an L-sequence.
2019 ◽
Vol 12
(03)
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pp. 1950044
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1973 ◽
Vol 51
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pp. 123-130
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1959 ◽
Vol 14
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pp. 223-234
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2013 ◽
Vol 89
(2)
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pp. 234-242
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2014 ◽
Vol 35
(7)
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pp. 2242-2268
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2011 ◽
Vol 11
(2)
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pp. 221-271
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1976 ◽
Vol 59
(1)
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pp. 29-29
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