American Research Journal of Mathematics

Simon Joseph1*, Isra Mukhtar2, Manal Juma3

Present panorama of the sequence of operators classes with their associated functional calculi, relevant in semi group theory: the sequence of operators of half plane, strip, sector and parabola-type. It is shown that the basic results in the theory of -semigroup (the Hille-Yosida and the Trotter-kato theorem) follow easily from general functional calculus principles by Markus Haase [9]. The introduction of parabola-type sequence of operators allows to treat cosine the sequence of operator’s functions by functional calculus methods.