Displaying similar documents to “Holomorphy types and spaces of entire functions of bounded type on Banach spaces”

Preduals of spaces of vector-valued holomorphic functions

Christopher Boyd (2003)

Czechoslovak Mathematical Journal

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For U a balanced open subset of a Fréchet space E and F a dual-Banach space we introduce the topology τ γ on the space ℋ ( U , F ) of holomorphic functions from U into F . This topology allows us to construct a predual for ( ℋ ( U , F ) , τ δ ) which in turn allows us to investigate the topological structure of spaces of vector-valued holomorphic functions. In particular, we are able to give necessary and sufficient conditions for the equivalence and compatibility of various topologies on spaces of vector-valued holomorphic...

Continuation of holomorphic solutions to convolution equations in complex domains

Ryuichi Ishimura, Jun-ichi Okada, Yasunori Okada (2000)

Annales Polonici Mathematici

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For an analytic functional S on ℂ n , we study the homogeneous convolution equation S * f = 0 with the holomorphic function f defined on an open set in ℂ n . We determine the directions in which every solution can be continued analytically, by using the characteristic set.

Solving singular convolution equations using the inverse fast Fourier transform

Eduard Krajník, Vincente Montesinos, Peter Zizler, Václav Zizler (2012)

Applications of Mathematics

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The inverse Fast Fourier Transform is a common procedure to solve a convolution equation provided the transfer function has no zeros on the unit circle. In our paper we generalize this method to the case of a singular convolution equation and prove that if the transfer function is a trigonometric polynomial with simple zeros on the unit circle, then this method can be extended.