Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-02-11T16:30:08.214Z Has data issue: false hasContentIssue false
  • English
  • Français

ODD–EVEN DECOMPOSITION OF FUNCTIONS

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

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
Check for updates
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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
Kuo, F. Y., Sloan, I. H., Wasilkowski, G. W. and Woźniakowski, H., ‘On decompositions of multivariate functions’, Math. Comput. 79(270) (2010), 953–966.CrossRefGoogle Scholar
Lomont, J. S., Applications of Finite Groups, corrected reprint of the 1959 original (Dover, New York, 1993).Google Scholar