Ioseb Gogodze and Koba Gelashvili

Representation Of c0-semigroups of Operators by a Chronological Integral

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.

Mathematics Subject Classification: 28B10, 47D03.

Key words and phrases: monoid, Riemann's chronological integral, formula of arrow inversion, formula of integration by parts, $c_0$-semigroup of operators, exponent.