The Series of Semigroup Theory Via Functional Calculus
1University of Juba, Faculty of Education, Department of Mathematics, South Sudan, Juba. 2Shaqra University, College of Science and Humanities (Girl Branch), Department of Mathematics, Al-Riyadh. 3Prince Sattam bin Abdulaziz University, College of Science and Humanity Studies (Girls Sections), Department of Mathematics, Kingdom of Saudi Arabia, Alkharj. University of Nyla, Faculty of Education, Department of Mathematics, Sudan
Simon Joseph, Isra Mukhtar, Manal Juma. “The Series of Semigroup Theory Via Functional Calculus”, American Research Journal of Mathematics. vol 4, no. 1, 2018, pp. 1-17.
Abstract
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.
