UGC Approved Journal no 63975(19)

ISSN: 2349-5162 | ESTD Year : 2014
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Published in:

Volume 5 Issue 6
June-2018
eISSN: 2349-5162

UGC and ISSN approved 7.95 impact factor UGC Approved Journal no 63975

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Published Paper ID:
JETIR1806841


Registration ID:
302086

Page Number

332-336

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Title

MATRIX REPRESENTATION OF MONOTONE CONVOLUTION

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Abstract

The monotone convolution of atomic measures is applied to the monotone product of matrix algebras. We prove here that the monotone convolution of m×m matrix and n×n marix becomes mn×mn matrix, which is a consequence of the algebraic construction of monotone product. We derive properties of atoms in the monotone convolution of atomic measures. We establish how moments change under the monotone convolution. We drive a differential equation about the minimum of support of a monotone convolution semigroup. We examine here that a property of a monotone convolution semigroup changes with respect to time parameter. Time-independent property is a property of a convolution semigroup. We derive that properties of non-commutative probability theory are time-independent. These properties are also time-independent in classical convolution semigroups. We classify strictly ⊳-stable distributions or equivalently, ⊳-infinitely divisible and self-similar distributions and show its equivalence to the free and Boolean cases.

Key Words

Monotone convolution, Convolution semigroups, Probability measures, Central measure, Symmetric measure, Gaussian measure, Cauchy transform.

Cite This Article

"MATRIX REPRESENTATION OF MONOTONE CONVOLUTION", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.5, Issue 6, page no.332-336, June-2018, Available :http://www.jetir.org/papers/JETIR1806841.pdf

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2349-5162 | Impact Factor 7.95 Calculate by Google Scholar

An International Scholarly Open Access Journal, Peer-Reviewed, Refereed Journal Impact Factor 7.95 Calculate by Google Scholar and Semantic Scholar | AI-Powered Research Tool, Multidisciplinary, Monthly, Multilanguage Journal Indexing in All Major Database & Metadata, Citation Generator

Cite This Article

"MATRIX REPRESENTATION OF MONOTONE CONVOLUTION", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.5, Issue 6, page no. pp332-336, June-2018, Available at : http://www.jetir.org/papers/JETIR1806841.pdf

Publication Details

Published Paper ID: JETIR1806841
Registration ID: 302086
Published In: Volume 5 | Issue 6 | Year June-2018
DOI (Digital Object Identifier): http://doi.one/10.1729/Journal.24772
Page No: 332-336
Country: Patna, Bihar, India .
Area: Engineering
ISSN Number: 2349-5162
Publisher: IJ Publication


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