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Funktsional'nyi Analiz i ego Prilozheniya, 2003, Volume 37, Issue 4, Pages 74–85
DOI: https://doi.org/10.4213/faa169
(Mi faa169)
 

This article is cited in 4 scientific papers (total in 4 papers)

On the Nonrepresentability of Functions of Several Variables by Quadratures

A. G. Khovanskii

Institute of Systems Analysis, Russian Academy of Sciences
Full-text PDF (185 kB) Citations (4)
References:
Abstract: The paper completes the construction of a multidimensional topological version of differential Galois theory. We construct a rich class of germs of functions of several variables which is closed under superpositions and other natural operations. The main theorem describes the behavior of the monodromy groups of such germs under the natural operations. As a result, we obtain topological obstructions to the representability of functions by quadratures, which give the strongest known statements about unsolvability of equations in closed form.
Keywords: multivalued function, monodromy group, differential Galois theory, representability by quadratures.
Received: 26.11.2002
English version:
Functional Analysis and Its Applications, 2003, Volume 37, Issue 4, Pages 302–310
DOI: https://doi.org/10.1023/B:FAIA.0000015580.92172.6c
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. G. Khovanskii, “On the Nonrepresentability of Functions of Several Variables by Quadratures”, Funktsional. Anal. i Prilozhen., 37:4 (2003), 74–85; Funct. Anal. Appl., 37:4 (2003), 302–310
Citation in format AMSBIB
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\paper On the Nonrepresentability of Functions of Several Variables by Quadratures
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Linking options:
  • https://www.mathnet.ru/eng/faa169
  • https://doi.org/10.4213/faa169
  • https://www.mathnet.ru/eng/faa/v37/i4/p74
  • This publication is cited in the following 4 articles:
    1. Askold Khovanskii, Springer Monographs in Mathematics, Topological Galois Theory, 2014, 107  crossref
    2. Askold Khovanskii, Springer Monographs in Mathematics, Topological Galois Theory, 2014, 195  crossref
    3. Casale G., “A New Proof of a Theorem of a. Khovanskii”, J. Dyn. Control Syst., 18:4 (2012), 449–454  crossref  mathscinet  zmath  isi  elib  scopus
    4. A. G. Khovanskii, “On solvability and unsolvability of equations in explicit form”, Russian Math. Surveys, 59:4 (2004), 661–736  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Функциональный анализ и его приложения Functional Analysis and Its Applications
     
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