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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The support of Mikusiński operators


Author: Thomas K. Boehme
Journal: Trans. Amer. Math. Soc. 176 (1973), 319-334
MSC: Primary 44A40
DOI: https://doi.org/10.1090/S0002-9947-1973-0313727-5
MathSciNet review: 0313727
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Abstract: A class of Mikusiński operators, called regular operators, is studied. The class of regular operators is strictly smaller than the class of all operators, and strictly larger than the class of all distributions with left bounded support. Regular operators have local properties. Lions' theorem of supports holds for regular operators with compact support. The fundamental solution to the Cauchy-Riemann equations is not regular, but the fundamental solution to the heat equation in two dimensions is regular and has support on a half-ray.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0313727-5
Keywords: Mikusiński operator, distribution, support, finite part, Cauchy-Riemann operator, heat operator
Article copyright: © Copyright 1973 American Mathematical Society

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