Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-08T23:33:28.807Z Has data issue: false hasContentIssue false
  • English
  • Français

The Weyl calculus and Clifford analysis

Published online by Cambridge University Press:  17 April 2009

Brian Jefferies  and
Alan McIntosh
Brian Jefferies
Affiliation:
School of MathematicsThe University of New South WalesSydney NSW 2052Australia e-mail: [email protected]
Alan McIntosh
Affiliation:
School of Mathematics, Physics, Computing and ElectronicsMacquarie UniversitySydney NSW 2109Australia e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The connection between Clifford analysis and the Weyl functional calculus for an n-tuple of bounded selfadjoint operators is noted. The operators do not necessarily commute with each other.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 2 , April 1998 , pp. 329 - 341
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Anderson, R.F.V., ‘The Weyl functional calculus’, J. Funct. Anal. 4 (1969), 240–267.CrossRefGoogle Scholar
[2]Anderson, R.F.V., ‘On the Weyl functional calculus’, J. Funct. Anal. 6 (1970), 110–115.CrossRefGoogle Scholar
[3]Brackx, F., Delanghe, R. and Sommen, F., Clifford analysis, Research Notes in Mathematics 76 (Pitman, Boston, London, Melbourne, 1982).Google Scholar
[4]Greiner, G. and Ricker, W., ‘Commutativity of compact operators’, Studia Math. 112 (1995), 109–125.Google Scholar
[5]Jefferies, B., McIntosh, A. and Picton-Warlow, J., ‘The monogenic functional calculus’ (to appear).Google Scholar
[6]Kisil, V.V., ‘Möbius transformations and monogenic functional calculus’, Electron. Res. Announc. Amer. Math. Soc. 2 (1996), 26–33.CrossRefGoogle Scholar
[7]McIntosh, A. and Pryde, A., ‘A functional calculus for several commuting operators’, Indiana Univ. Math. J. 36 (1987), 421–439.CrossRefGoogle Scholar
[8]Nelson, E., ‘A functional calculus for non-commuting operators’, in Functional analysis and related fields, (Browder, F.E., Editor), Proceedings of a conference in honour of Professor Marshal Stone, Univ. of Chicago, May 1968 (Springer-Verlag, Berlin, Heidelberg, New York, 1970), pp. 172–187.Google Scholar
[9]Taylor, M.E., ‘Functions of several self-adjoint operators’, Proc. Amer. Math. Soc. 19 (1968), 91–98.Google Scholar