Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
The principal purpose of this thesis is to develop and study several functional calculi for commuting unbounded operators. This is achieved by combining and generalising the
 

Summary: Summary
The principal purpose of this thesis is to develop and study several functional calculi
for commuting unbounded operators. This is achieved by combining and generalising the
works of Taylor [41,42], M c Intosh [30,31], and Cowling et al. [11]. However, we also
obtain, under special circumstances, an explicit expression for Taylor's functional calculus;
and utilise various functional calculi to give a different outlook to the work of Dore and
Venni [14].
Let us now briefly look at Taylor [41,42], M c Intosh [30,31], and Cowling et al. [11].
We will then mention what we have achieved, before giving an outline of the thesis.
Consider Taylor [41,42]. In these papers Taylor introduced a notion of a joint spectrum
and defined a functional calculus for a commuting tuple of bounded operators on a Banach
space. This work generalised the spectrum and functional calculus for a single operator,
and the work by Shilov [38], Arens [4], Arens--Calderon [5], and Waelbrock [45]. Later,
Putinar [35] showed the uniqueness of Taylor's functional calculus. Vasilescu [44] showed
how to extend the notion of joint spectrum to D­commuting systems, and Vasilescu [43]
and Janas [24] obtained explicit formulae for the functional calculus.
Now, consider M c Intosh [30]. In this paper M c Intosh developed a functional calculus
for type ! operators, which we will call sector type ! operators, in a Hilbert space. This
functional calculus provided a simple means to derive the basic properties of semigroups
and fractional powers, of these operators. It also provides, by the consideration of quadratic

  

Source: Albrecht, David - Caulfield School of Information Technology, Monash University

 

Collections: Computer Technologies and Information Sciences