The analytic-functional calculus for several commuting operators

Functional Calculus for Non-Commuting Operators

A Functional Calculus for Pairs of Commuting Polynomially Bounded Operators

A functional calculus valid for the class of absolutely continuous pairs of commuting polynomially bounded operators is defined.

The functional calculus for commuting row contractions

A commuting row contraction is a d-tuple of commuting operators T1, . . . , Td such that ∑d i=1 TiT ∗ i ≤ I. Such operators have a polynomial functional calculus which extends to a norm closed algebra of multipliers Ad on Drury-Arveson space. We characterize those row contractions which admit an extension of this map to a weak-∗ continuous functional calculus on the full multiplier algebra. In ...

H∞-calculus for the Sum of Non-commuting Operators

A recent result of Kalton and Weis is extended to the case of noncommuting operators, employing the commutator condition of Labbas and Terreni, or of Da Prato and Grisvard. Under appropriate assumptions it is shown that the sum of two non-commuting operators admits an H∞-calculus. The main results are then applied to a parabolic problem on a wedge domain.

The Riesz-Clifford Functional Calculus for Non-Commuting Operators and Quantum Field Theory

We present a Riesz-like hyperholomorphic functional calculus for a set of non-commuting operators based on the Clifford analysis. Applications to the quantum field theory are described. This work was partially supported by CONACYT Project 1821-E9211, Mexico. On leave from the Odessa State University.