Chapter

Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations

Volume 221 of the series Operator Theory: Advances and Applications pp 617-634

Date:

Holomorphy in Multicomplex Spaces

  • D. C. StruppaAffiliated withSchmid College of Science and Technology, Chapman University Email author 
  • , A. VajiacAffiliated withSchmid College of Science and Technology, Chapman University
  • , M. B. VajiacAffiliated withSchmid College of Science and Technology, Chapman University

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Abstract

In this paper we extend our research on bicomplex holomorphy and on the existence of bicomplex differential operators to the nested space of multicomplex numbers.S pecifically, we will discuss the different sets of idempotent representations for multicomplex numbers and we will use them to develop a theory of holomorphic and multicomplex analytic functions.

Keywords

Bicomplex algebra PDE systems computational algebra resolutions syzygy