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  • 1
    Electronic Resource
    Electronic Resource
    Local operators between spaces of ultradifferentiable functions and ultradistributions (1982)
    Springer
    Manuscripta mathematica 38 (1982), S. 131-161 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this article we characterize certain ultradifferential operators by the condition of being local. First, we examine the continuity properties of local linear operators on spaces of ultradifferentiable functions in the sense of Beurling and of Roumieu. Next, a structure theorem for vector-valued ultradistributions with support at the origin is proved. This result leads to a representation theorem for continuous local operators from spaces of ultradifferentiable functions into various spaces of ultradistributions. In combination with the continuity results we thus obtain in many cases the desired characterization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01168588
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