Communications of the Korean Mathematical Society (대한수학회논문집)
- Volume 9 Issue 3
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- Pages.607-616
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- 1994
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
REPRESENTATION OF THE GENERALIZED FUNCTIONS OF GELFAND AND SHILOV
- Jae Young Chung (Department of Mathematics, Kunsan National University, Kunsan, Chunbuk 573-360, Korea) ;
- Sung Jin Lee (Department of Mathematics, Daejin University, Pochun, 487-800, Korea)
- Published : 1994.07.01
Abstract
I. M. Gelfand and G. E. Shilov [GS] introduced the Gelfand-Shilov spaces of type S, generalized type S and type W of test functions to investigate the uniqueness of the solutions of the Cauchy problems of partial differential equations. Using the heat kernel method Matsuzawa gave structure theorems for distributions, hyperfunctions and generalized functions in the dual space $(S^s_r)'$ of the Gelfand-Shilov space of type S in [M1, M2 and DM], respectively. Also, we gave structure theorems for ultradistributions, Fourier hyperfunctions in [CK, KCK], respectively.
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