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Strong Boehmians


Authors: Ellen R. Dill and Piotr Mikusiński
Journal: Proc. Amer. Math. Soc. 119 (1993), 885-888
MSC: Primary 44A40
DOI: https://doi.org/10.1090/S0002-9939-1993-1152275-8
MathSciNet review: 1152275
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Abstract: A new class of generalized functions is introduced. The objects are defined as convolution quotients. The space is larger than the space of Schwartz distributions but smaller than the space of Boehmians.


References [Enhancements On Off] (What's this?)

  • [1] R. P. Boas, Entire functions, Academic Press, New York, 1954. MR 0068627 (16:914f)
  • [2] T. K. Boehme, On sequences of continuous functions and convolution, Studia Math. 25 (1965), 333-335. MR 0178311 (31:2569)
  • [3] -, The support of Mikusiński operators, Trans. Amer. Math. Soc. 176 (1973), 319-334. MR 0313727 (47:2281)
  • [4] J. Burzyk, Nonharmonic solutions of the Laplace equation, Generalized Functions, Convergence Structures and their Applications, Plenum Press, New York and London, 1988, pp. 3-11. MR 975712 (90f:46064)
  • [5] E. R. Dill, Strong Boehmians, research report, Dept. of Math., Univ. of Central Florida, 1991.
  • [6] J. Mikusiński and P. Mikusiński, Quotients de suites et leurs applications dans l'analyse fonctionnelle, C. R. Acad. Sci. Paris Sér. I Math. 293 (1981), 463-464. MR 646866 (83a:46048)
  • [7] P. Mikusiński, Convergence of Boehmians, Japan. J. Math. (N.S.) 9 (1983), 159-179. MR 722539 (85h:46063)
  • [8] -, Boehmians and generalized functions, Acta Math. Hungar. 51 (1988), 271-281. MR 956979 (90a:46090)
  • [9] -, On harmonic Boehmians, Proc. Amer. Math. Soc. 106 (1989), 447-449. MR 960649 (90b:44007)
  • [10] D. Nemzer, Periodic Boehmians, Internat. J. Math. Math. Sci. 12 (1989), 685-692. MR 1024971 (90k:44006)
  • [11] -, Periodic generalized functions, Rocky Mountain J. Math. 20 (1990). MR 1073715 (92a:44003)
  • [12] -, Periodic Boehmians. II, Bull. Austrian Math. Soc. 44 (1991), 271-278. MR 1126366 (92h:46059)
  • [13] W. Rudin, Real and complex analysis, 2nd ed., McGraw-Hill, New York, 1974. MR 0344043 (49:8783)
  • [14] A. H. Zemanian, Realizability theory for continuous linear systems, Academic Press, New York, 1972. MR 0449807 (56:8108)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1152275-8
Keywords: Boehmian, convolution quotient, Schwartz distributions
Article copyright: © Copyright 1993 American Mathematical Society

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