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Product integral in a Fréchet algebra. (English) Zbl 1155.46309

Summary: Product integral of locally summable function in a Fréchet algebra is defined and some of its properties are proved. The main tool is the Arens-Michael representation of Fréchet algebra which allows us to extend the notion of the product integral from a Banach to Fréchet algebra.

MSC:

46J99 Commutative Banach algebras and commutative topological algebras
28B99 Set functions, measures and integrals with values in abstract spaces
34G99 Differential equations in abstract spaces
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