Abstract:
We propose a modification of the previously-known abstract scheme that reduces the problem of expansion of elements of a locally convex space in series over the system of eigenvectors of some linear operator to the question of existence of a nontrivial expansion of zero in this space. We implement this general scheme for the spaces of analytic functions in domains of the extended complex plane and the systems of simple fractions that are the eigenfunctions of the Pommier operator.
Keywords:
absolutely representing system, nontrivial expansion of zero, generalized Laplace transform, representation and convolution operator, Pommier operator, Wolff–Denjoy series.
Citation:
V. B. Sherstyukov, “Nontrivial expansions of zero and representation of analytic functions by series of simple fractions”, Sibirsk. Mat. Zh., 48:2 (2007), 458–473; Siberian Math. J., 48:2 (2007), 369–381
\Bibitem{She07}
\by V.~B.~Sherstyukov
\paper Nontrivial expansions of zero and representation of analytic functions by series of simple fractions
\jour Sibirsk. Mat. Zh.
\yr 2007
\vol 48
\issue 2
\pages 458--473
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\transl
\jour Siberian Math. J.
\yr 2007
\vol 48
\issue 2
\pages 369--381
\crossref{https://doi.org/10.1007/s11202-007-0039-8}
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Linking options:
https://www.mathnet.ru/eng/smj39
https://www.mathnet.ru/eng/smj/v48/i2/p458
This publication is cited in the following 6 articles:
S. N. Melikhov, “Coefficients of exponential series for analytic functions and the Pommiez operator”, J. Math. Sci. (N. Y.), 257:2 (2021), 206–245
O. A. Ivanova, S. N. Melikhov, “On operators which commute with the Pommiez type operator in weighted spaces of entire functions”, St. Petersburg Math. J., 28:2 (2017), 209–224
O. A. Ivanova, S. N. Melikhov, “On A. F. Leont'ev's interpolating function”, Ufa Math. J., 6:3 (2014), 17–27
V. B. Sherstyukov, “Dual characterization of absolutely representing systems in inductive limits of Banach spaces”, Siberian Math. J., 51:4 (2010), 745–754
A. L. Myl'nikov, “Minimal Involution-Free Nongroup Reduced Twisted Subsets”, Math. Notes, 88:6 (2010), 860–867
A. L. Myl'nikov, “Minimal non-group twisted subsets containing involutions”, Algebra and Logic, 46:4 (2007), 250–262
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