Functional equations in real-analytic functions

G. Belitskii; V. Tkachenko

Studia Mathematica (2000)

  • Volume: 143, Issue: 2, page 153-174
  • ISSN: 0039-3223

Abstract

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The equation φ (x) = g(x,φ (x)) in spaces of real-analytic functions is considered. Connections between local and global aspects of its solvability are discussed.

How to cite

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Belitskii, G., and Tkachenko, V.. "Functional equations in real-analytic functions." Studia Mathematica 143.2 (2000): 153-174. <http://eudml.org/doc/216814>.

@article{Belitskii2000,
abstract = {The equation φ (x) = g(x,φ (x)) in spaces of real-analytic functions is considered. Connections between local and global aspects of its solvability are discussed.},
author = {Belitskii, G., Tkachenko, V.},
journal = {Studia Mathematica},
keywords = {functional equations in a single variable; analytic functions; solvability conditions; fixed points; multi-dimensional examples},
language = {eng},
number = {2},
pages = {153-174},
title = {Functional equations in real-analytic functions},
url = {http://eudml.org/doc/216814},
volume = {143},
year = {2000},
}

TY - JOUR
AU - Belitskii, G.
AU - Tkachenko, V.
TI - Functional equations in real-analytic functions
JO - Studia Mathematica
PY - 2000
VL - 143
IS - 2
SP - 153
EP - 174
AB - The equation φ (x) = g(x,φ (x)) in spaces of real-analytic functions is considered. Connections between local and global aspects of its solvability are discussed.
LA - eng
KW - functional equations in a single variable; analytic functions; solvability conditions; fixed points; multi-dimensional examples
UR - http://eudml.org/doc/216814
ER -

References

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  1. [BL] G. Belitskii and Yu. Lyubich, The real-analytic solutions of the Abel functional equation, Studia Math. 134 (1999), 135-141. Zbl0924.39012
  2. [BB] G. Belitskii and N. Bikov, Spaces of cohomologies associated with linear functional equations, Ergodic Theory Dynam. Systems 18 (1998), 343-356. 
  3. [BT1] G. Belitskii and V. Tkachenko, Analytic solvability of multidimensional functional equations in a neighborhood of a nonsingular point, Teor. Funktsiǐ Funktsional. Anal. i Prilozhen. 59 (1993), 7-21 (in Russian). Zbl0907.39023
  4. [BT2] G. Belitskii and V. Tkachenko, On solvability of linear difference equations in smooth and real-analytic vector functions of several variables, Integral Equations Oper. Theory 18 (1994), 124-129. Zbl0803.39002
  5. [B] A. D. Bryuno, Analytic form of differential equations, Trudy Moskov. Mat. Obshch. 25 (1973), 119-262 (in Russian). Zbl0263.34003
  6. [G] H. Grauert, On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math. 68 (1958), 460-472. Zbl0108.07804
  7. [H] L. Hörmander, An Introduction to Complex Analysis in Several Variables, van Nostrand, Princeton, 1966. 
  8. [I] Yu. Il'yashenko (ed.), Nonlinear Stokes Phenomena, Adv. in Soviet Math. 14 Amer. Math. Soc., 1996. 
  9. [N] Z. Nitecki, Differentiable Dynamics, MIT Press, Cambridge, Mass., 1971. Zbl0246.58012
  10. [S] W. Smajdor, Local analytic solutions of the functional equation φ (z) = h(z,φ (f(z))) in multidimensional spaces, Aequationes Math. 1 (1968), 20-36. Zbl0157.46001
  11. [W] H. Whitney, Differentiable manifolds, Ann. of Math. 37 (1936), 645-680. Zbl62.1454.01

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