Bicomplex Holomorphic Functional Calculus

Document Type

Article

Publication Date

2014

Abstract

In this paper we introduce and study a functional calculus for bicomplex linear bounded operators. The study is based on the decomposition of bicomplex numbers and of linear operators using the two nonreal idempotents. We show that, due to the presence of zero divisors in the bicomplex numbers, the spectrum of a bounded operator is unbounded. We therefore introduce a different spectrum (called reduced spectrum) which is bounded and turns out to be the right tool to construct the bicomplex holomorphic functional calculus. Finally we provide some properties of the calculus.

Comments

This article was originally published in Mathematische Nachrichten, volume 287, in 2014. DOI: 10.1002/mana.201200354

Peer Reviewed

1

Copyright

Wiley

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