An extension of the complex–real (C–R) calculus to the bicomplex setting, with applications

Daniel Alpay; Kamal Diki; Mihaela Vajiac

doi:10.1002/mana.202200475

An extension of the complex–real (C–R) calculus to the bicomplex setting, with applications

Daniel Alpay, Kamal Diki, Mihaela Vajiac

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this paper, we extend notions of complex (Formula presented.) -calculus to the bicomplex setting and compare the bicomplex polyanalytic function theory to the classical complex case. Applications of this theory include two bicomplex least mean square algorithms, which extend classical real and complex least mean square algorithms.

Original language	English
Pages (from-to)	454-481
Number of pages	28
Journal	Mathematische Nachrichten
Volume	297
Issue number	2
DOIs	https://doi.org/10.1002/mana.202200475
State	Published - 1 Feb 2024
Externally published	Yes

Keywords

BC−R$\mathbb {BC}-\mathbb {R}$ calculus
BLMS algorithm
C–R calculus
bicomplex gradient operator
bicomplex numbers

ASJC Scopus subject areas

General Mathematics

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10.1002/mana.202200475

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abstract = "In this paper, we extend notions of complex (Formula presented.) -calculus to the bicomplex setting and compare the bicomplex polyanalytic function theory to the classical complex case. Applications of this theory include two bicomplex least mean square algorithms, which extend classical real and complex least mean square algorithms.",

keywords = "BC−R\$\textbackslash{}mathbb \{BC\}-\textbackslash{}mathbb \{R\}\$ calculus, BLMS algorithm, C–R calculus, bicomplex gradient operator, bicomplex numbers",

author = "Daniel Alpay and Kamal Diki and Mihaela Vajiac",

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AU - Diki, Kamal

AU - Vajiac, Mihaela

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Y1 - 2024/2/1

N2 - In this paper, we extend notions of complex (Formula presented.) -calculus to the bicomplex setting and compare the bicomplex polyanalytic function theory to the classical complex case. Applications of this theory include two bicomplex least mean square algorithms, which extend classical real and complex least mean square algorithms.

AB - In this paper, we extend notions of complex (Formula presented.) -calculus to the bicomplex setting and compare the bicomplex polyanalytic function theory to the classical complex case. Applications of this theory include two bicomplex least mean square algorithms, which extend classical real and complex least mean square algorithms.

KW - BC−R$\mathbb {BC}-\mathbb {R}$ calculus

KW - BLMS algorithm

KW - C–R calculus

KW - bicomplex gradient operator

KW - bicomplex numbers

UR - https://www.scopus.com/pages/publications/85165107483

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An extension of the complex–real (C–R) calculus to the bicomplex setting, with applications

Abstract

Keywords

ASJC Scopus subject areas

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