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Hermitian Clifford Analysis

In: Operator Theory

Author

Listed:
  • Irene Sabadini

    (Politecnico di Milano, Dipartimento di Matematica)

  • Frank Sommen

    (Ghent University, Department of Mathematical Analysis)

Abstract

This paper gives an overview of some basic results on Hermitian Clifford analysis, a refinement of classical Clifford analysis dealing with functions in the kernel of two mutually adjoint Dirac operators invariant under the action of the unitary group. The set of these functions, called Hermitian monogenic, contains the set of holomorphic functions in several complex variables. The paper discusses, among other results, the Fischer decomposition, the Cauchy–Kovalevskaya extension problem, the axiomatic radial algebra, and also some algebraic analysis of the system associated with Hermitian monogenic functions. While the Cauchy–Kovalevskaya extension problem can be carried out for the Hermitian monogenic system, this system imposes severe constraints on the initial Cauchy data. There exists a subsystem of the Hermitian monogenic system in which these constraints can be avoided. This subsystem, called submonogenic system, will also be discussed in the paper.

Suggested Citation

  • Irene Sabadini & Frank Sommen, 2015. "Hermitian Clifford Analysis," Springer Books, in: Daniel Alpay (ed.), Operator Theory, edition 127, chapter 55, pages 1581-1608, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0667-1_13
    DOI: 10.1007/978-3-0348-0667-1_13
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