On the formulations of the quaternionic functional calculus

Journal of Geometry and Physics

Volumn 60, Issue 10, 2010, Pages 1490-1508

  Colombo, Fabrizio ^a   Sabadini, Irene ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

Cauchy formula for right slice regular functions; Closed linear operators; Left and right linear operators; Quaternionic functional calculus; S resolvent operator; S spectrum

Indexed keywords

EID: 77954377621     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.geomphys.2010.05.014     Document Type: Article

References (29)

1. Colombo F., Gentili G., Sabadini I., Struppa D.C. A functional calculus in a non commutative setting. Electron. Res. Announc. Math. Sci 2007, 14:60-68.
2. F. Colombo, G. Gentili, I. Sabadini, D.C. Struppa, Non commutative functional calculus: bounded operators, Compl. Anal. Oper. Theory (2010), in press (). doi:10.1007/s11785-009-0015-3.
3. Colombo F., Gentili G., Sabadini I., Struppa D.C. Non commutative functional calculus: unbounded operators. J. Geom. Phys. 2010, 60:251-259.
4. Colombo F., Gentili G., Sabadini I., Struppa D.C. An overview on functional calculi in different settings. Trends in Mathematics 2009, 69-99. Birkhäuser.
5. Gentili G., Struppa D.C. A new theory of regular functions of a quaternionic variable. Adv. Math. 2007, 216:279-301.
6. Colombo F., Sabadini I. On some properties of the quaternionic functional calculus. J. Geom. Anal. 2009, 19:601-627.
7. Colombo F., Sabadini I. A structure formula for slice monogenic functions and some of its consequences. Trends in Mathematics 2009, 101-114. Birkhäuser.
8. Adler S. Quaternionic Quantum Field Theory 1995, Oxford University Press.
9. F. Colombo, I. Sabadini, The quaternionic evolution operator, 2009, preprint.
10. F. Colombo, I. Sabadini, The Cauchy formula with s-monogenic kernel and a functional calculus for noncommuting operators, 2008, preprint.
11. Colombo F., Sabadini I., Struppa D.C. Slice monogenic functions. Israel J. Math. 2009, 171:385-403.
12. Colombo F., Sabadini I., Struppa D.C. Extension properties for slice monogenic functions. Israel J. Math. 2010, 177:369-389.
13. F. Colombo, I. Sabadini, D.C. Struppa, Duality theorems for slice hyperholomorphic functions, J. Reine Angew. Math., 2010 (in press).
14. Colombo F., Sabadini I., Struppa D.C. A new functional calculus for noncommuting operators. J. Funct. Anal. 2008, 254:2255-2274.
15. Jefferies B., McIntosh A. The Weyl calculus and Clifford analysis. Bull. Austral. Math. Soc. 1998, 57:329-341.
16. Jefferies B., McIntosh A., Picton-Warlow J. The monogenic functional calculus. Studia Math. 1999, 136:99-119.
17. Kisil V.V., Ramirez de Arellano E. The Riesz-Clifford functional calculus for noncommuting operators and quantum field theory. Math. Methods Appl. Sci. 1996, 19:593-605.
18. McIntosh A., Pryde A. A functional calculus for several commuting operators. Indiana Univ. Math. J. 1987, 36:421-439.
19. Jefferies B. Spectral Properties of Noncommuting Operators. Lecture Notes in Mathematics 2004, vol. 1843. Springer-Verlag, Berlin.
20. Brackx F., Delanghe R., Sommen F. Clifford analysis. Pitman Res. Notes in Math. 1982, 76.
21. Colombo F., Sabadini I., Sommen F., Struppa D.C. Analysis of Dirac Systems and Computational Algebra. Progress in Mathematical Physics 2004, vol. 39. Birkhäuser, Boston.
22. F.H. Vasilescu, Analytic functional calculus and spectral decompositions, Translated from the Romanian, Mathematics and its Applications (East European Series), 1. D. Reidel Publishing Co., Dordrecht; Editura Academiei Republicii Socialiste Romania, Bucharest.
23. Kenneth R., Zarouf D., Fouad Z. Incompatibility of compact perturbations with the Sz. Nagy-Foias functional calculus. Proc. Amer. Math. Soc. 1994, 121:519-522.
24. Taylor J.L. The analytic-functional calculus for several commuting operators. Acta Math. 1970, 125:1-38.
25. Taylor J.L. Functions of several noncommuting variables. Bull. Amer. Math. Soc. 1973, 79:1-34.
26. Dunford N., Schwartz J. Linear Operators, Part I: General Theory 1988, J. Wiley and Sons.
27. Rudin W. Functional Analysis. Functional Analysis. McGraw-Hill Series in Higher Mathematics 1973, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg.
28. Colombo F., Gentili G., Sabadini I. A Cauchy kernel for slice regular functions. Ann. Glob. Anal. Geom. 2010, 37:361-378.
29. Anderson F.W., Fuller K.R. Rings and Categories of Modules 1992, Springer Verlag, New York. 2nd ed.