Representation of \(c_0\)-semigroups of operators by a chronological integral. (English) Zbl 0908.47038

Gogodze, Ioseb K.; Gelashvili, Koba N.

Mem. Differ. Equ. Math. Phys. 11, 47-66 (1997).

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

Keywords:

monoid; arrow inversion; integration by parts; \(c_0\)-semigroup of operators; right and left chronological integrals; exponential function; chronological exponent