Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B.
Advisors: Dmitry S. Kaliuzhnyi-Verbovetskyi Committee members: Joseph A. Ball; Robert P. Boyer; Anatolli Grinshpan; Hugo J. Woerdeman.
Özet:
This thesis extends some standard results familiar from undergraduate calculus to the setting of higher order noncommutative functions. These extensions are accomplished using a difference-differential operator in a completely algebraic, topological free, manner. The results include a version of the mean value theorem, the Taylor formula and an antiderivative. The Taylor formula is applied to obtain results about power series on nilpotent matrices and higher order polynomials.