Analytical Theory of Semi-groups

Abstract

The analytical theory of semi-groups of bounded linear operators in a B-space deals with the exponential functions in infinite dimensional function spaces. It is concerned with the problem of determining the most general bounded linear operator valued function T(t), t≧ 0, which satisfies the equations

$$T\left( {t + s} \right)T{\kern 1pt} = T\left( t \right) \cdot T\left( s \right),\,T\left( 0 \right){\kern 1pt} = I$$