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Vector-valued almost automorphic distributions and vector-valued almost automorphic ultradistributions. (English) Zbl 1473.46046

Summary: In this paper, we introduce the notions of a vector-valued almost automorphic distribution and a vector-valued almost automorphic ultradistribution, working in the framework of complex Banach spaces. We prove several structural characterizations for the introduced classes.

MSC:

46F05 Topological linear spaces of test functions, distributions and ultradistributions
42A75 Classical almost periodic functions, mean periodic functions
43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
35B15 Almost and pseudo-almost periodic solutions to PDEs
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References:

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