Fischer decomposition of the space of entire functions for the convolution operator |
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Authors: | V V Napalkov A U Mullabaeva |
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Institution: | 1.Institute of Mathematics and Computer Center, Ufa Scientific Center,Russian Academy of Sciences,Ufa, Bashkortostan,Russia;2.Bashkir State University, Bashkortostan, Russia,Ufa, Bashkortostan,Russia |
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Abstract: | It is known that any function in a Hilbert Bargmann–Fock space can be represented as the sum of a solution of a given homogeneous differential equation with constant coefficients and a function being a multiple of the characteristic function of this equation with conjugate coefficients. In the paper, a decomposition of the space of entire functions of one complex variable with the topology of uniform convergence on compact sets for the convolution operator is presented. As a corollary, a solution of the de la Vallée Poussin interpolation problem for the convolution operator with interpolation points at the zeros of the characteristic function with conjugate coefficient is obtained. |
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