Cm semialgebraic sections over the plane

Charles Fefferman; Garving K. Luli

doi:10.2969/jmsj/86258625

C^m semialgebraic sections over the plane

Charles Fefferman
, Garving K. Luli

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper we settle the two-dimensional case of a conjecture involving unknown semialgebraic functions with specified smoothness. More precisely, we prove the following result: Let H be a semialgebraic bundle with respect to C_loc^m (R², R^D). If H has a section, then it has a semialgebraic section.

Original language	English (US)
Pages (from-to)	759-811
Number of pages	53
Journal	Journal of the Mathematical Society of Japan
Volume	74
Issue number	3
DOIs	https://doi.org/10.2969/jmsj/86258625
State	Published - Jul 2022

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

semialgebraic functions
semialgebraic sections
system of linear equations

Access to Document

10.2969/jmsj/86258625

Cite this

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title = "Cm semialgebraic sections over the plane",

abstract = "In this paper we settle the two-dimensional case of a conjecture involving unknown semialgebraic functions with specified smoothness. More precisely, we prove the following result: Let H be a semialgebraic bundle with respect to Clocm (R2, RD). If H has a section, then it has a semialgebraic section.",

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AB - In this paper we settle the two-dimensional case of a conjecture involving unknown semialgebraic functions with specified smoothness. More precisely, we prove the following result: Let H be a semialgebraic bundle with respect to Clocm (R2, RD). If H has a section, then it has a semialgebraic section.

KW - semialgebraic functions

KW - semialgebraic sections

KW - system of linear equations

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