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- Second Hyperfunctions, Regular Sequences, and Fourier Inverse Transforms
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Second Hyperfunctions, Regular Sequences, and Fourier Inverse Transforms
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Abstract
Second hyperfunctions are formal boundary values of microfunctions with holomorphic parameters defined on wedges in much the same way in which classical hyperfunctions are boundary values of holomorphic functions defined on wedges. Since microfunctions with holomorphic parameters are themselves already defined in a formal way, second hyperfunctions have a rather non-intuitive definition and few explicit examples of second hyperfunctions which are not classical are known. In this paper we shall show that one can arrive at a better understanding by introducing the notion of regular sequences of holomorphic functions. We shall then show that representation of second hyperfunctions in terms of regular sequences is quite efficient in the context of regularization of the Fourier-inverse transform of functions which appear in second microlocalization.
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About: Otto Liess
Universita di Bologna, Dipartimento di Matematica, Piazza Porta S. Donato 5, 40127 Bologna, Italy, liess@dm.unibo.it
About: Yasunori Okada
Chiba University, Department of Mathematics, Yayoi 1-33, Inage-ku, Chiba 263-8522, Japan, okada@math.s.chiba-u.ac.jp
About: Nobuyuki Tose
Keio University, Hiyoshi Campus, Hiyoshi 4-1-1, Kohoku, Yokohama 223-8521, Japan, tose@math.hc.keio.ac.jp