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The monogenic functional calculus

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EN
Abstrakty
EN
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.
Twórcy
  • School of Mathematics, Physics, Computing and Electronics, Macquarie University, Sydney, NSW 2109, Australia
Bibliografia
  • [1] R. F. V. Anderson, The Weyl functional calculus, J. Funct. Anal. 4 (1969), 240-267.
  • [2] F. Brackx, R. Delanghe and F. Sommen, Clifford Analysis, Pitman Res. Notes Math. Ser. 76, Pitman, Boston, 1982.
  • [3] B. Jefferies and A. McIntosh, The Weyl calculus and Clifford analysis, Bull. Austral. Math. Soc. 57 (1998), 329-341.
  • [4] B. Jefferies and B. Straub, Lacunas in the support of the Weyl calculus for two hermitian matrices, submitted.
  • [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.
  • [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.
  • [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.
  • [10] A. McIntosh, A. Pryde and W. Ricker, Comparison of joint spectra for certain classes of commuting operators, Studia Math. 88 (1988), 23-36.
  • [11] J. Ryan, Plemelj formulae and transformations associated to plane wave decompositions in complex Clifford analysis, Proc. London Math. Soc. 64 (1992), 70-94.
  • [12] F. Sommen, Plane wave decompositions of monogenic functions, Ann. Polon. Math. 49 (1988), 101-114.
  • [13] J. L. Taylor, The analytic-functional calculus for several commuting operators, Acta Math. 125 (1970), 1-38.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv136i2p99bwm
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