On harmonic Boehmians

On harmonic Boehmians
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Proc. Amer. Math. Soc. 106 (1989), 447-449

DOI: https://doi.org/10.1090/S0002-9939-1989-0960649-X

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Existence of generalized functions (called Boehmians) satisfying the Laplace equation which are not ${C^\infty }$-functions is proved.

References

T. K. Boehme, On sequences of continuous functions and convolution, Studia Math. 25 (1965), 333–335. MR 178311, DOI 10.4064/sm-25-3-333-335
Thomas K. Boehme, The support of Mikusiński operators, Trans. Amer. Math. Soc. 176 (1973), 319–334. MR 313727, DOI 10.1090/S0002-9947-1973-0313727-5
Józef Burzyk, A Paley-Wiener type theorem for regular operators of bounded support, Studia Math. 93 (1989), no. 3, 187–200. MR 1030487, DOI 10.4064/sm-93-3-187-200
Piotr Mikusiński, Convergence of Boehmians, Japan. J. Math. (N.S.) 9 (1983), no. 1, 159–179. MR 722539, DOI 10.4099/math1924.9.159
P. Mikusiński, Boehmians and generalized functions, Acta Math. Hungar. 51 (1988), no. 3-4, 271–281. MR 956979, DOI 10.1007/BF01903334
Piotr Mikusiński, Fourier transform for integrable Boehmians, Rocky Mountain J. Math. 17 (1987), no. 3, 577–582. MR 908263, DOI 10.1216/RMJ-1987-17-3-577
P. Mikusiński, Boehmians on open sets, Acta Math. Hungar. 55 (1990), no. 1-2, 63–73. MR 1077060, DOI 10.1007/BF01951388

Value of a Boehmian at a point

The Boehmians as an

-space

Dennis Nemzer, Periodic generalized functions, Rocky Mountain J. Math. 20 (1990), no. 3, 657–669. MR 1073715, DOI 10.1216/rmjm/1181073091
Walter Rudin, Functional analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. MR 0365062