Functional equations in real-analytic functions
Belitskii, G. ; Tkachenko, V.
Studia Mathematica, Tome 141 (2000), p. 153-174 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:216814 
@article{bwmeta1.element.bwnjournal-article-smv143i2p153bwm,
     author = {G. Belitskii and V. Tkachenko},
     title = {Functional equations in real-analytic functions},
     journal = {Studia Mathematica},
     volume = {141},
     year = {2000},
     pages = {153-174},
     zbl = {0967.39009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv143i2p153bwm}
}

Belitskii, G.; Tkachenko, V. Functional equations in real-analytic functions. Studia Mathematica, Tome 141 (2000) pp. 153-174. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv143i2p153bwm/

[000] [BL] G. Belitskii and Yu. Lyubich, The real-analytic solutions of the Abel functional equation, Studia Math. 134 (1999), 135-141. | Zbl 0924.39012

[001] [BB] G. Belitskii and N. Bikov, Spaces of cohomologies associated with linear functional equations, Ergodic Theory Dynam. Systems 18 (1998), 343-356.

[002] [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). | Zbl 0907.39023

[003] [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. | Zbl 0803.39002

[004] [B] A. D. Bryuno, Analytic form of differential equations, Trudy Moskov. Mat. Obshch. 25 (1973), 119-262 (in Russian). | Zbl 0263.34003

[005] [G] H. Grauert, On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math. 68 (1958), 460-472. | Zbl 0108.07804

[006] [H] L. Hörmander, An Introduction to Complex Analysis in Several Variables, van Nostrand, Princeton, 1966.

[007] [I] Yu. Il'yashenko (ed.), Nonlinear Stokes Phenomena, Adv. in Soviet Math. 14 Amer. Math. Soc., 1996.

[008] [N] Z. Nitecki, Differentiable Dynamics, MIT Press, Cambridge, Mass., 1971. | Zbl 0246.58012

[009] [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. | Zbl 0157.46001

[010] [W] H. Whitney, Differentiable manifolds, Ann. of Math. 37 (1936), 645-680. | Zbl 62.1454.01