Solvability of Convolution Operators | Zendy

Yasunori Okada | Zendy

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Solvability of Convolution Operators

Author(s) -

Yasunori Okada

Publication year - 1994

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195166127

Subject(s) - mathematics , convolution (computer science) , convolution power , algebra over a field , pure mathematics , calculus (dental) , mathematical analysis , artificial intelligence , computer science , orthodontics , fourier transform , medicine , fourier analysis , artificial neural network , fractional fourier transform

We study the Surjectivity of convolution operators on the spaces of hyperfunctions and Fourier hyperfunctions. On the space of hyperfunctions, we give a sufficient condition (the kernel is a nonzero ultradistribution), weaker than earlier conditions. On the space of Fourier hyperfunction, we give a new sufficient condition and new necessary conditions for the Surjectivity. Especially in one dimensional case, they become a sufficient and necessary condition. To this aim we use the Fourier analysis as in L. Ehrenpreis [E-2] and T. Kawai [Ka-1]. Communicated by T. Kawai, November 16, 1992, Revised April 26, 1993. 1991 Mathematics Subject Classification : 42A85, 46F15. College of Arts and Sciences, Chiba University, 1-33 Yayoi-cho Inage-ku, Chiba 263 Japan.

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