Positive Definite and Related Functions in the Product of Hypercomplex Systems

Positive Definite and Related Functions in the Product of Hypercomplex Systems

Hossam A. Ghany

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A.S. Okb El Bab

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A.M. Zabel

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M. Zakarya

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Helwan University

Al-Azhar University

Positive Definite and Related Functions in the Product of Hypercomplex Systems

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Abstract

The main aim of this paper is to explore harmonic properties of functions defined in the product of hypercomplex systems. By means of the generalized translation operators, the precise definition of the product of commutative hypercomplex systems is given and full description for its properties are shown. The integral representations of positive definite function defined in the product of commutative normal hypercomplex systems are given. Furthermore, we present the necessary and sufficient conditions guarantees the property of positive definite function in the product of hypercomplex systems.

References

23 Cites in Article

Reference Format

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

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How to Cite This Article

Hossam A. Ghany. 2017. \u201cPositive Definite and Related Functions in the Product of Hypercomplex Systems\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 17 (GJSFR Volume 17 Issue F2): .

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GJSFR Volume 17 Issue F2
Pg. 49- 61

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords

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Classification

GJSFR-F Classification: MSC 2010: 43A62, 43A22, 43A10.

Submission ReceivedJanuary 17, 2017
Peer Review Double Blind
Handling Editor
Accepted February 16, 2017
Published February 27, 2017

Version of record

v1.2

Issue date

March 24, 2017

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Article Matrices

Total Score: 104

Country: Egypt

Subject: Global Journal of Science Frontier Research - F: Mathematics & Decision

Authors: A.S. Okb El Bab, A.M. Zabel, Hossam A. Ghany, M. Zakarya (PhD/Dr. count: 0)

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Total Views: 3314

Total Downloads: 1703

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