Banach space valued ultradistributions and applications to abstract Cauchy problems
نویسنده
چکیده
We define the convolution of Banach space valued ultradistributions in the sense of Braun, Meise, and Taylor. We then treat abstract Cauchy problems in Banach spaces as convolution equations and give a characterization of those problems that have ultradistributional fundamental solutions. Our characterization extends in the Beurling case a result due to H.A. Emamirad. We apply our result to differential operators in Banach spaces of ultradifferentiable functions with different (e.g. ultradifferential) boundary conditions.
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تاریخ انتشار 2009