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ODD–EVEN DECOMPOSITION OF FUNCTIONS

Part of: Rings with polynomial identity Nontrigonometric harmonic analysis Nonparametric inference Combinatorial probability Distribution theory - Probability Rings and algebras with additional structure Functions of several variables

Published online by Cambridge University Press:  08 January 2020

IOSIF PINELIS Open the ORCID record for IOSIF PINELIS [Opens in a new window]
IOSIF PINELIS*
Affiliation:
Department of Mathematical Sciences, Michigan Technological University, Houghton, Michigan 49931, USA email ipinelis@mtu.edu
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Abstract

The main result of this note implies that any function from the product of several vector spaces to a vector space can be uniquely decomposed into the sum of mutually orthogonal functions that are odd in some of the arguments and even in the other arguments. Probabilistic notions and facts are employed to simplify statements and proofs.

Keywords

even and odd functionsinvolutionsorthogonal decompositionsignal extraction

MSC classification

Primary: 26B40: Representation and superposition of functions
Secondary: 16R50: Other kinds of identities (generalized polynomial, rational, involution) 16W10: Rings with involution; Lie, Jordan and other nonassociative structures 39B55: Orthogonal additivity and other conditional equations 42C05: Orthogonal functions and polynomials, general theory 60C05: Combinatorial probability 60E05: Distributions 62G86: Nonparametric inference and fuzziness
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 1 , August 2020 , pp. 104 - 108
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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References

Ierley, G. and Kostinski, A., ‘Universal rank-order transform to extract signals from noisy data’, Phys. Rev. X 9 (2019), Article ID 031039, 28 pages.Google Scholar
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Lomont, J. S., Applications of Finite Groups, corrected reprint of the 1959 original (Dover, New York, 1993).Google Scholar