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Representation of \(c_0\)-semigroups of operators by a chronological integral. (English) Zbl 0908.47038
Summary: Right and left chronological integrals are defined for a function of real variable whose domain of values is endowed with minimal algebraic and limiting structures. It is proved that an exponential function of a linear (possibly unbounded) operator can be represented by means of a chronological integral which preserves a number of properties of a chronological exponent.
MSC:
47D06 One-parameter semigroups and linear evolution equations
28B10 Group- or semigroup-valued set functions, measures and integrals
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