**Ioseb Gogodze and Koba Gelashvili**

## Representation Of *c*_{0}-semigroups of Operators by a Chronological Integral

**abstract:**

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.