Non Commutative Functional Calculus: Bounded Operators
By Fabrizio Colombo, Graziano Gentili, Irene Sabadini, Daniele C. Struppa. 2007
48 citations recorded by the source corpus.
In this paper we develop a functional calculus for bounded operators defined on quaternionic Banach spaces. This calculus is based on the new notion of slice-regularity, see Gentili and Struppa (Acad Sci Paris 342:741–744, 2006) and the key tools are a new resolvent operator and a new eigenvalue problem.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/be8de7466066fe7456a685128694dfcd40d4e4b6
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Irene Sabadini
- Fabrizio Colombo
- Daniele C. Struppa
- Caterina Stoppato
- Graziano Gentili
- Daniel Alpay
- Riccardo Ghiloni
- A. Perotti
In Computational Theory and Mathematics
- Fabrizio Colombo
- Irene Sabadini
- Daniel Alpay
- Daniele C. Struppa
- Caterina Stoppato
- Graziano Gentili
- Omar Abu Arqub
- Nabil T. Shawagfeh
Citations in the corpus
- A Cauchy kernel for slice regular functions (2009, background): “Keywords Non-commutative and regular Cauchy kernel · Slice regular quaternionic functions · Representation formula for regular functions Mathematical Subject Classification 2000 30G35”
- Schur Functions and Their Realizations in the Slice Hyperholomorphic Setting (2011, background): “For some results on the quaternionic functional calculus we refer the reader to [34, 37, 39, 41].”
- Entire slice regular functions (2015, background): “The S-functional calculus, see [9, 45, 48, 49, 59, 60, 61, 71], is the analogue of the Riesz-Dunford functional calculus in the quaternionic setting.”
- Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions (2012, unknown): “[16, 18, 21]; while slice monogenic functions admit a functional calculus for n-tuples of operators, see [24, 20, 22].”
- On Some Properties of the Quaternionic Functional Calculus (2009, methodology): “23 holds also for Laurent power series expansions, in [10] we could prove that for open sets U ⊃ σS(T ) satisfying (a) and (b) the integral (10) does not depend on the choice of the imaginary unit I ∈ S and on U .”
- Power series and analyticity over the quaternions (2009, background): “Hence the theory of regular quaternionic functions, which is quickly developing, reveals a new feature that reminds the nice properties of holomorphic complex functions.”