Complexity Classes of Analytic Functions and Their Tangent Spaces

Abstract A number of results on the nonrepresentability of analytic functions of two variables as superpositions of functions of one variable are obtained. The method of proof is based on a description of tangent spaces to complexity classes and properties of linear superpositions.

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Journal
Mathematical Notes
Published
2026-09-30
DOI
https://doi.org/10.1134/s0001434626604533
Primary Topic
Computability, Logic, AI Algorithms
Type
article
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article

Complexity Classes of Analytic Functions and Their Tangent Spaces

V. K. Beloshapka
Mathematical Notes
Computability, Logic, AI Algorithms
article

Complexity Classes of Analytic Functions and Their Tangent Spaces

V. K. Beloshapka
article en

Abstract

Abstract A number of results on the nonrepresentability of analytic functions of two variables as superpositions of functions of one variable are obtained. The method of proof is based on a description of tangent spaces to complexity classes and properties of linear superpositions.

Mathematical NotesVol. 120(5-6)
Lomonosov Moscow State University (RU), Moscow Center of Fundamental and Applied Mathematics (RU)
Reduced inequalities
Openalex Percentile: Top 9%
Computability, Logic, AI Algorithms
DOISourceOpenAlex
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Complexity Classes of Analytic Functions and Their Tangent Spaces — V. K. Beloshapka · Mathematical Notes (2026) | TGRS Research Map | TGRS