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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2026. Vol 55

On the Establishment of the Order of Smoothness of the Minimal Concave Continuation of a Real Discrete Function Defined on the Vertices of a Parallelepiped

Author(s)

Dostonjon N. Barotov

Financial University under the Government of the Russian Federation, Moscow, Russian Federation

Abstract
In this paper, we study the order of differentiability of the minimal concave continuation to an n-dimensional coordinate parallelepiped of a real discrete function defined on the vertices of this arbitrary n-dimensional coordinate parallelepiped. As a result of the study, the order of differentiability of the minimal concave continuation to an n-dimensional coordinate parallelepiped of a real discrete function defined on the vertices of this arbitrary n-dimensional coordinate parallelepiped is established, namely, it is proved that if a given real discrete function can be represented as a linear combination of its discrete variables, then its minimal concave continuation is linear and, therefore, infinitely differentiable on an n-dimensional coordinate parallelepiped, and if it cannot be represented as a linear combination of its discrete variables, then its minimal concave continuation on an n-dimensional coordinate parallelepiped is only continuous.
About the Authors
Dostonjon N. Barotov, Senior Lecturer, Financial University under the Government of the Russian Federation, Moscow, 109456, Russian Federation, DNBarotov@fa.ru
For citation
Barotov D. N. On the Establishment of the Order of Smoothness of the Minimal Concave Continuation of a Real Discrete Function Defined on the Vertices of a Parallelepiped. The Bulletin of Irkutsk State University. Series Mathematics, 2026, vol. 55, pp. 80–93. (in Russian) https://doi.org/10.26516/1997-7670.2026.55.80
Keywords
order of smoothness of a function, minimal concave continuation of a discrete function, Boolean-like function
UDC
519.716.32, 517.518.244, 512.563
MSC
06E30, 26B25, 03B50
DOI
https://doi.org/10.26516/1997-7670.2026.55.80
References


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