Periodic hyperfunctions and Fourier series
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- by Soon-Yeong Chung, Dohan Kim and Eun Gu Lee PDF
- Proc. Amer. Math. Soc. 128 (2000), 2421-2430 Request permission
Abstract:
Every periodic hyperfunction is a bounded hyperfunction and can be represented as an infinite sum of derivatives of bounded continuous periodic functions. Also, Fourier coefficients $c_{\alpha }$ of periodic hyperfunctions are of infra-exponential growth in $\mathbb {R}^{n}$, i.e., $c_{\alpha }< C_{\epsilon }e^{\epsilon |\alpha |}$ for every $\epsilon >0$ and every $\alpha \in \mathbb {Z}^{n}$. This is a natural generalization of the polynomial growth of the Fourier coefficients of distributions. To show these we introduce the space $\mathcal {B}_{L^{p}}$ of hyperfunctions of $L^{p}$ growth which generalizes the space $\mathcal {D}’_{L^{p}}$ of distributions of $L^{p}$ growth and represent generalized functions as the initial values of smooth solutions of the heat equation.References
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Additional Information
- Soon-Yeong Chung
- Affiliation: Department of Mathematics, Sogang University, Seoul 121–742, Korea
- Email: sychung@ccs.sogang.ac.kr
- Dohan Kim
- Affiliation: Department of Mathematics, Seoul National University, Seoul 151–742, Korea
- Email: dohankim@snu.ac.kr
- Eun Gu Lee
- Affiliation: Department of Mathematics, Dongyang Technical College, Seoul 152–714, Korea
- Email: eglee@orient.dytc.ac.kr
- Received by editor(s): June 16, 1998
- Received by editor(s) in revised form: September 24, 1998
- Published electronically: December 7, 1999
- Additional Notes: Partially supported by BSRI and GARC–KOSEF
- Communicated by: Christopher D. Sogge
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2421-2430
- MSC (1991): Primary 46F15, 35K05, 42B05
- DOI: https://doi.org/10.1090/S0002-9939-99-05281-8
- MathSciNet review: 1657782