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Spin Geometry, Clifford Analysis, and Joint Seminormality

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Advances in Analysis and Geometry

Part of the book series: Trends in Mathematics ((TM))

Abstract

The first part of this article studies the integral and maximal operators associated with fundamental solutions of Dirac operators on Clifford bundles. The main goal is to obtain explicit estimates for integral transforms of this kind in terms of the corresponding maximal functions. As direct cones-quences of such estimates one derives several quantitative Hartogs-Rosenthal type theorems concerning monogenic approximation on compact sets.

The second part illustrates a Clifford analysis approach to the theory of seminormal systems of Hilbert space operators. The four existing concepts of joint seminormality are reevaluated by assuming that the remainders in some Bochner-Kodaira identities are semidefinite, and a new concept is introduced based on a Bochner-Weitzenböck identity. A rather general singular integral model of jointly seminormal pairs of systems of self-adjoint operators that involves Riesz transforms is presented, and a Putnam type commutator inequality for that model is proved.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Baker University, Baldwin City, Kansas, 66006, USA

    Mircea Martin

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  1. Mircea Martin
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Editor information

Editors and Affiliations

  1. Faculty of Science and Technology, University of Macau, 3001, Macau, China

    Tao Qian

  2. Basel, Switzerland

    Thomas Hempfling

  3. Centre for Mathematics and its Applications Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, Australia

    Alan McIntosh

  4. Department of Mathematical Analysis, University of Ghent, Galglaan 2, Ghent, 9000, Belgium

    Frank Sommen

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Martin, M. (2004). Spin Geometry, Clifford Analysis, and Joint Seminormality. In: Qian, T., Hempfling, T., McIntosh, A., Sommen, F. (eds) Advances in Analysis and Geometry. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7838-8_12

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  • DOI: https://doi.org/10.1007/978-3-0348-7838-8_12

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9589-7

  • Online ISBN: 978-3-0348-7838-8

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