# The monogenic functional calculus

Brian Jefferies; Alan McIntosh; James Picton-Warlow

Studia Mathematica (1999)

- Volume: 136, Issue: 2, page 99-119
- ISSN: 0039-3223

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topJefferies, Brian, McIntosh, Alan, and Picton-Warlow, James. "The monogenic functional calculus." Studia Mathematica 136.2 (1999): 99-119. <http://eudml.org/doc/216667>.

@article{Jefferies1999,

abstract = {A study is made of a symmetric functional calculus for a system of bounded linear operators acting on a Banach space. Finite real linear combinations of the operators have real spectra, but the operators do not necessarily commute with each other. Analytic functions of the operators are formed by using functions taking their values in a Clifford algebra.},

author = {Jefferies, Brian, McIntosh, Alan, Picton-Warlow, James},

journal = {Studia Mathematica},

keywords = {functional calculus; Clifford algebra; monogenic function; monogenic functional calculus},

language = {eng},

number = {2},

pages = {99-119},

title = {The monogenic functional calculus},

url = {http://eudml.org/doc/216667},

volume = {136},

year = {1999},

}

TY - JOUR

AU - Jefferies, Brian

AU - McIntosh, Alan

AU - Picton-Warlow, James

TI - The monogenic functional calculus

JO - Studia Mathematica

PY - 1999

VL - 136

IS - 2

SP - 99

EP - 119

AB - A study is made of a symmetric functional calculus for a system of bounded linear operators acting on a Banach space. Finite real linear combinations of the operators have real spectra, but the operators do not necessarily commute with each other. Analytic functions of the operators are formed by using functions taking their values in a Clifford algebra.

LA - eng

KW - functional calculus; Clifford algebra; monogenic function; monogenic functional calculus

UR - http://eudml.org/doc/216667

ER -

## References

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- [3] B. Jefferies and A. McIntosh, The Weyl calculus and Clifford analysis, Bull. Austral. Math. Soc. 57 (1998), 329-341. Zbl0915.47015
- [4] B. Jefferies and B. Straub, Lacunas in the support of the Weyl calculus for two hermitian matrices, submitted. Zbl1059.47016
- [5] V. V. Kisil, Möbius transformations and monogenic functional calculus, ERA Amer. Math. Soc. 2 (1996), 26-33.
- [6] V. V. Kisil and E. Ramírez de Arellano, The Riesz-Clifford functional calculus for non-commuting operators and quantum field theory, Math. Methods Appl. Sci. 19 (1996), 593-605. Zbl0853.47012
- [7] C. Li, A. McIntosh and T. Qian, Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces, Rev. Mat. Iberoamericana 10 (1994), 665-721. Zbl0817.42008
- [8] A. McIntosh and A. Pryde, The solution of systems of operator equations using Clifford algebras, in: Miniconf. on Linear Analysis and Function Spaces 1984, Centre for Mathematical Analysis, ANU, Canberra, 9 (1985), 212-222.
- [9] A. McIntosh and A. Pryde, A functional calculus for several commuting operators, Indiana Univ. Math. J. 36 (1987), 421-439. Zbl0694.47015
- [10] A. McIntosh, A. Pryde and W. Ricker, Comparison of joint spectra for certain classes of commuting operators, Studia Math. 88 (1988), 23-36. Zbl0665.47002
- [11] J. Ryan, Plemelj formulae and transformations associated to plane wave decompositions in complex Clifford analysis, Proc. London Math. Soc. 64 (1992), 70-94. Zbl0703.30043
- [12] F. Sommen, Plane wave decompositions of monogenic functions, Ann. Polon. Math. 49 (1988), 101-114. Zbl0673.30038
- [13] J. L. Taylor, The analytic-functional calculus for several commuting operators, Acta Math. 125 (1970), 1-38. Zbl0233.47025

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