The quaternionic evolution operator

Advances in Mathematics

Volumn 227, Issue 5, 2011, Pages 1772-1805

  Colombo, Fabrizio ^a   Sabadini, Irene ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

Bounded and unbounded quaternionic generators; Hille Phillips Yosida theorem in the quaternionic setting; Quaternionic group; Quaternionic semigroup; Right and left linear quaternionic operators; S resolvent operator; S spectrum

Indexed keywords

EID: 79956359162     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2011.04.001     Document Type: Article

References (25)

1. Adler S. Quaternionic Quantum Field Theory 1995, Oxford University Press.
2. Anderson F.W., Fuller K.R. Rings and Categories of Modules 1992, Springer-Verlag, New York. second ed.
3. Brackx F., Delanghe R., Sommen F. Clifford Analysis. Pitman Res. Notes Math. 1982, vol. 76.
4. Colombo F., Gentili G., Sabadini I., Struppa D.C. Extension results for slice regular functions of a quaternionic variable. Adv. Math. 2009, 222:1793-1808.
5. Colombo F., Gentili G., Sabadini I. A Cauchy kernel for slice regular functions. Ann. Global Anal. Geom. 2010, 37:361-378.
6. Colombo F., Gentili G., Sabadini I., Struppa D.C. Non commutative functional calculus: bounded operators. Complex Anal. Oper. Theory 2010, 4:821-843.
7. Colombo F., Gentili G., Sabadini I., Struppa D.C. Non commutative functional calculus: unbounded operators. J. Geom. Phys. 2010, 60:251-259.
8. Colombo F., Sabadini I. A structure formula for slice monogenic functions and some of its consequences. Trends Math. 2009, 101-114. Birkhäuser.
9. Colombo F., Sabadini I. On some properties of the quaternionic functional calculus. J. Geom. Anal. 2009, 19:601-627.
10. Colombo F., Sabadini I. On the formulations of the quaternionic functional calculus. J. Geom. Phys. 2010, 60:1490-1508.
11. Colombo F., Sabadini I. The Cauchy formula with s-monogenic kernel and a functional calculus for noncommuting operators. J. Math. Anal. Appl. 2011, 373:655-679.
12. Colombo F., Sabadini I., Sommen F., Struppa D.C. Analysis of Dirac Systems and Computational Algebra. Prog. Math. Phys. 2004, vol. 39. Birkhäuser, Boston.
13. Colombo F., Sabadini I., Struppa D.C. A new functional calculus for noncommuting operators. J. Funct. Anal. 2008, 254:2255-2274.
14. Colombo F., Sabadini I., Struppa D.C. Slice monogenic functions. Israel J. Math. 2009, 171:385-403.
15. Colombo F., Sabadini I., Struppa D.C. An extension theorem for slice monogenic functions and some of its consequences. Israel J. Math. 2010, 177:369-389.
16. Colombo F., Sabadini I., Struppa D.C. Duality theorems for slice hyperholomorphic functions. J. Reine Angew. Math. 2010, 645:85-104.
17. Colombo F., Sabadini I., Struppa D.C. Noncommutative Functional Calculus. Progr. Math. 2011, vol. 289. Birkhäuser, Basel.
18. Dunford N., Schwartz J. Linear Operators, Part I: General Theory 1988, J. Wiley and Sons.
19. Gentili G., Struppa D.C. A new theory of regular functions of a quaternionic variable. Adv. Math. 2007, 216:279-301.
20. Ghiloni R., Perotti A. Slice regular functions on real alternative algebras. Adv. Math. 2011, 226:1662-1691.
21. Jefferies B. Spectral Properties of Noncommuting Operators. Lecture Notes in Math. 2004, vol. 1843. Springer-Verlag, Berlin.
22. Jefferies B., McIntosh A. The Weyl calculus and Clifford analysis. Bull. Aust. Math. Soc. 1998, 57:329-341.
23. Jefferies B., McIntosh A., Picton-Warlow J. The monogenic functional calculus. Studia Math. 1999, 136:99-119.
24. McIntosh A., Pryde A. A functional calculus for several commuting operators. Indiana Univ. Math. J. 1987, 36:421-439.
25. Rudin W. Functional Analysis. McGraw-Hill Ser. Higher Math. 1973, McGraw-Hill Book Co., New York, Düsseldorf, Johannesburg.