Malagutti, Marcello;
(2024)
Regularity and Semialgebraicity of Solutions of Linear EquationsSystems.
Bruno Pini Mathematical Analysis Seminar
, 14
(2)
pp. 201-228.
10.6092/issn.2240-2829/18866.
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Abstract
This work is concerned with the study of a necessary and sufficient condition for the existence of solutions with a given regularity to a system of linear equations with coefficients of given regularity. First, to properly contextualize the subject matter and to introduce crucial analytical solving tools, we go through results by C.Fefferman- J.Kollár and by C.Fefferman - G.K.Luli. Then we prove our result to determine a necessary and sufficient condition for the existence of continuous (C0) semialgebraic solutions in case of a system of linear equations with continuous semialgebraic coefficients.
| Type: | Article |
|---|---|
| Title: | Regularity and Semialgebraicity of Solutions of Linear EquationsSystems |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.6092/issn.2240-2829/18866 |
| Publisher version: | https://doi.org/10.6092/issn.2240-2829/18866 |
| Language: | English |
| Additional information: | Copyright (c) 2024 Marcello Malagutti. This work is licensed under a Creative Commons Attribution 3.0 Unported License. |
| Keywords: | Linear equations system, semialgebraic solution, Glaeser refinement, bundle section, semialgebraic set |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10185490 |
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