Abstract:
In the space of entire functions we study an interpolation problem with multiplicity by the functions from a closed subspace which is invariant in respect to the operator of differentiation. The discrete set of the nodes for the interpolation with multiplicity is located on the real axis in the complex plane. The proof is based on the passage from the subspace to its subspace consisting of all series of exponentials converging in the topology of uniform convergence on compact sets. We obtain a criterion for the solvability of the interpolation problem with real nodes having multiplicity by series of exponentials in the terms of location of exponents of exponentials.
Keywords:
entire function, interpolation with multiplicity, series of exponents, ideal, Fischer representation.
Citation:
S. G. Merzlyakov, S. V. Popenov, “Interpolation with multiplicity by series of exponentials in $H(\mathbb C)$ with nodes on the real axis”, Ufa Math. J., 5:3 (2013), 127–140
\Bibitem{MerPop13}
\by S.~G.~Merzlyakov, S.~V.~Popenov
\paper Interpolation with multiplicity by series of exponentials in $H(\mathbb C)$ with nodes on the real axis
\jour Ufa Math. J.
\yr 2013
\vol 5
\issue 3
\pages 127--140
\mathnet{http://mi.mathnet.ru/eng/ufa214}
\crossref{https://doi.org/10.13108/2013-5-3-127}
\elib{https://elibrary.ru/item.asp?id=20930805}
Linking options:
https://www.mathnet.ru/eng/ufa214
https://doi.org/10.13108/2013-5-3-127
https://www.mathnet.ru/eng/ufa/v5/i3/p130
This publication is cited in the following 8 articles:
S. G. Merzlyakov, “Interpolation by Generalized Exponential Series”, Math. Notes, 109:1 (2021), 94–101
S. G. Merzlyakov, “Interpolation and absolutely convergent series in Fréchet spaces”, Sb. Math., 210:1 (2019), 105–144
S. G. Merzlyakov, S. V. Popenov, “Interpolation by series of exponential functions whose exponents are condensed in a certain direction”, J. Math. Sci. (N. Y.), 257:3 (2021), 334–352
Merzlyakov S.G. Popenov S.V., “Interpolation By Sums of Series of Exponentials and Global Cauchy Problem For Convolution Operators”, Dokl. Math., 99:2 (2019), 149–151
S. G. Merzlyakov, S. V. Popenov, “Interpolation by series of exponentials in $H(D)$ with real nodes”, Ufa Math. J., 7:1 (2015), 46–57
V. V. Napalkov, A. U. Mullabaeva, “Kratnaya interpolyatsionnaya zadacha Valle Pussena”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:1 (2015), 63–77
V. V. Napalkov, K. R. Zimens, “Zadacha Valle Pussena v yadre operatora svertki na poluploskosti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:2 (2015), 283–292
K. R. Zimens, V. V. Napalkov, “The multiple de la Vallée-Poussin problem on convex domains in the kernel of the convolution operator”, Dokl. Math., 90:2 (2014), 581–583
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