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Funktsional. Anal. i Prilozhen., 2003, Volume 37, Issue 4, Pages 74–85 (Mi faa169)  

This article is cited in 2 scientific papers (total in 2 papers)

On the Nonrepresentability of Functions of Several Variables by Quadratures

A. G. Khovanskii

Institute of Systems Analysis, Russian Academy of Sciences

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

DOI: https://doi.org/10.4213/faa169

Full text: PDF file (185 kB)
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English version:
Functional Analysis and Its Applications, 2003, 37:4, 302–310

Bibliographic databases:

UDC: 517.9
Received: 26.11.2002

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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\pages 74--85
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. 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
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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