We calculate the local Fourier transforms for connections on the formal punctured disk, reproducing the results of J. Fang and C. Sabbah using a different method. Our method is similar to Fang’s, but more direct.
Alexander V. AbaninSouthern Institute of Mathematics, Southern Federal UniversityRyuichi IshimuraGraduate School of Science, Chiba UniversityLe Hai KhoiDivision of Mathematical Sciences School of Physical and Mathematical Sciences, Nanyang Technological University
Functional AnalysisSpectral Theory and Operator Algebramathscidoc:1701.12017
Alexander V Abanin · Hai Khoi. Exponential-polynomial bases for null spaces of convolution operators in A −∞. 2011.
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Alexander V Abanin · Le Hai Khoi. Linear continuous right inverse to convolution operator in spaces of holomorphic functions of polynomial growth. 2015.
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A V Abanin · Hai Khoi · S Nalbandyan. Full length article Minimal absolutely representing systems of exponentials for A −∞ (Ω ). 2011.
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Napalkov V V. ON DISCRETE WEAKLY SUFFICIENT SETS IN CERTAIN SPACES OF ENTIRE FUNCTIONS[J]. Mathematics of The Ussr-izvestiya, 1982, 19(2): 349-357.
We consider the convolution operators in spaces of functions which are holomorphic in a bounded convex domain in ℂ^{$n$}and have a polynomial growth near its boundary. A characterization of the surjectivity of such operators on the class of all domains is given in terms of low bounds of the Laplace transformation of analytic functionals defining the operators.