Pointwise Functional Calculi

Operator Theory - Spectra and Functional Calculi

The Timer Cascade: Functional Modelling and Real Time Calculi

Case studies can significantly contribute towards improving the understanding of formalisms and thereby to their applicability in practice. One such case, namely a cascade of the familiar 24-hour timers (in suitably generalized form) provides interesting gedanken experiments and illustrations for presenting, illustrating and comparing various formalisms for modelling real-time behaviour of syst...

Holomorphic Functional Calculi and Sums of Commuting Operators

Let S and T be commuting operators of type ! and type $ in a Banach space X. Then the pair has a joint holomorphic functional calculus in the sense that it is possible to deene operators f(S; T) in a consistent manner, when f is a suitable holomorphic function deened on a product of sectors. In particular, this gives a way to deene the sum S +T when ! +$ <. We show that this operator is always ...

Action Calculi III : Higher-order Calculi

This paper extends an arbitrary action calculus [11] to higher order, in a way which parallels the extension of the -calculus [13] to higher order by Sangiorgi [18]. Action calculi are a subclass of action structures [10], which in turn are an enriched class of monoidal categories. Each action calculus AC(K) is distinguished by its set K of controls and their reaction rules. The notion of actio...

Coconvex pointwise approximation

There are two kinds of estimates of the degree of approximation of continuous functions on [−1, 1] by algebraic polynomials, Nikolskii-type pointwise estimates and Jackson-type uniform estimates, involving either ordinary moduli of smoothness, or the DitzianTotik (DT) ones, or the recent estimates involving the weighted DTmoduli of smoothness. The purpose of this paper is to complete the table ...