# Functional equations in real-analytic functions

Studia Mathematica (2000)

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

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topBelitskii, 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

top- [BL] G. Belitskii and Yu. Lyubich, The real-analytic solutions of the Abel functional equation, Studia Math. 134 (1999), 135-141. Zbl0924.39012
- [BB] G. Belitskii and N. Bikov, Spaces of cohomologies associated with linear functional equations, Ergodic Theory Dynam. Systems 18 (1998), 343-356.
- [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
- [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
- [B] A. D. Bryuno, Analytic form of differential equations, Trudy Moskov. Mat. Obshch. 25 (1973), 119-262 (in Russian). Zbl0263.34003
- [G] H. Grauert, On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math. 68 (1958), 460-472. Zbl0108.07804
- [H] L. Hörmander, An Introduction to Complex Analysis in Several Variables, van Nostrand, Princeton, 1966.
- [I] Yu. Il'yashenko (ed.), Nonlinear Stokes Phenomena, Adv. in Soviet Math. 14 Amer. Math. Soc., 1996.
- [N] Z. Nitecki, Differentiable Dynamics, MIT Press, Cambridge, Mass., 1971. Zbl0246.58012
- [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
- [W] H. Whitney, Differentiable manifolds, Ann. of Math. 37 (1936), 645-680. Zbl62.1454.01

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