Composing infinitely differentiable functions
Article
Received:
Accepted:
- 100 Downloads
Keywords
Banach Space Differentiable Function Orlicz Space Inductive Limit Nonlinear Integral Equation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Appell, J.: Implicit functions, nonlinear integral equations, and the measure of noncompactness of the superposition operators. J. Math. Anal. Appl.83, 1, 251–263 (1981)MATHCrossRefMathSciNetGoogle Scholar
- 2.Appell, J. De Pascale, E.: Lipschitz and Darbo conditions for the superposition operator in some non-ideal spaces of differentiable functions, Annali Mat. Pura Appl. (to appear)Google Scholar
- 3.Appell, J., Massabò, I., Vignoli, A., Zabrejko, P.P.: Lipschitz and Darbo conditions for the superposition operator in ideal spaces. Annali Mat. Pura Appl.152, 123–137 (1988)MATHCrossRefGoogle Scholar
- 4.Appell, J., Zabrejko, P.P.: Nonlinear superposition operators. Cambridge: Cambridge University Press 1990MATHGoogle Scholar
- 5.Berkolajko, M.Z.: On a nonlinear operator acting in generalized Hölder spaces. (Russian), Voronezh. Gos. Univ. Trudy Sem. Funk. Anal.12, 96–104 (1969)Google Scholar
- 6.Dzhanashiya, G.A.: On the Carleman problem for Gevrey function classes (Russian), Doklady Akad. Nauk SSSR145, 2, 259–262 (1962) [=Soviet Math.,Doklady3 969–972 (1962)]MathSciNetGoogle Scholar
- 7.Dzhanashiya, G.A.: On the superposition of two functions from Gevrey function classes. (Russian), Soobsh. Akad. Nauk Gruz. SSR33, 257–262 (1964)Google Scholar
- 8.Fraenkel, L.E.: Formulae for high derivatives of composite functions. Math. Proc. Cambridge Philos. Soc.83, 159–165 (1978)MATHMathSciNetGoogle Scholar
- 9.Friedman, A.: Generalized functions and partial differential equations. Englewood Cliffs, New Jersey: Prentice-Hall, 1963MATHGoogle Scholar
- 10.Gevrey, M.: Sur la nature analytique des solutions des équations aux dérivées partielles. Ann. Ecole Norm. Sup. Paris35, 129–190 (1918)MathSciNetGoogle Scholar
- 11.Ider, M.: On the superposition of functions in Carleman classes. Bull. Austral. Math. Soc.39, 471–476 (1989)MATHMathSciNetCrossRefGoogle Scholar
- 12.Krasnosel'skij, M.A.: Topological methods in the theory of nonlinear integral equations. (Russian), Moscow: Gostekhizdat 1956; [Engl. transl.: New York: McMillan 1964]Google Scholar
- 13.Krasnosel'skij, M.A., Rutitskij, Y.B.: Convex functions and Orlicz spaces. (Russian), Moscow: Fizmatgiz 1958 [Engl. transl.: Noordhoff, Groningen 1961]Google Scholar
- 14.Krasnosel'skij, M.A., Rutitskij, Y.B., Sultanov, R.M.: On a nonlinear operator acting in a space of abstract functions. (Russian), Izv. Akad. Nauk Azerb. SSR3, 15–21 (1959)Google Scholar
- 15.Krasnosel'skij, M.A., Vajnikko, G.M., Zabrejko, P.P., Rutitskij, Y.B., Stetsenko, V.Y.: Approximate solutions of operator equations. (Russian), Moscow: Nauka 1969 [Engl. transl.: Groningen: Noordhoff 1972]Google Scholar
- 16.Lichawski, K., Matkowski, J., Miś, J.: Locally defined operators in the space of differentiable functions. Univ. Bielsko-Biała 1988 (preprint)Google Scholar
- 17.Lions, J.-L., Magenes, E.: Problèmes aux limites non homogènes et aplications III. Paris: Dunod 1970Google Scholar
- 18.Mandelbrojt, S.: Séries adhérentes, régularisation de suites, applications. Paris: Gauthier-Villars 1952Google Scholar
- 19.Mishina, A.P.: Propuryanov, I.V.: Higher algebra. (Russian), Moscow: Nauka 1965MATHGoogle Scholar
- 20.Mityagin, B.S.: An indefinitely differentiable function with the values of its derivatives given at a point. (Russian), Doklady Akad. Nauk SSSR138, 2, 289–292 (1961) [=Soviet Math., Doklady2, 594–597 (1961)Google Scholar
- 21.Nazarov, V.I.: The superposition operator in Roumieu spaces of infinitely differentiable functions. (Russian), Izv. Akad. Nauk BSSR5, 22–28 (1984)Google Scholar
- 22.Nazarov, V.I.: A nonlinear differential equation of first order in Roumieu spaces. (Russian), Doklady Akad. Nauk BSSR28, 780–783 (1984)MATHGoogle Scholar
- 23.Northcott, D.G.: Multilinear algebra, Cambridge: Cambridge University Press 1984MATHGoogle Scholar
- 24.Riordan, J.: Combinatorial identities. New York. Wiley 1967Google Scholar
- 25.Roman, S.: The formula of Faà di Bruno. Am. Math. Monthly87, 805–809 (1980)MATHCrossRefMathSciNetGoogle Scholar
- 26.Roumieu, C.: Sur quelques extensions de la notion de distributions. Ann. Ecole Norm. Sup. Paris77, 47–121 (1960)MathSciNetGoogle Scholar
- 27.Sadovskij, B.N.: Limit-compact and condensing operators. (Russian), Uspekhi Mat. Nauk27, 1, 81–146 (1972) [=Russ. Math. Surv.27, 85–155 (1972)]MATHGoogle Scholar
- 28.Shilov, G.Y.: Differentiability of functions in linear spaces. (With an appendix by P.P. Zabrejko). (Russian), Yaroslav. Gos. Univ. 6–120 (1978)Google Scholar
- 29.Silva, J.S.: Su certe classi di spazi localmente convessi importanti per le applicazioni. Roma: Rend. Mat. Univ.14, 388–410 (1955)Google Scholar
- 30.Zabrejko, P.P.: Ideal function spaces I (Russian), Vestinik: Yaroslav. Gos. Univ.8, 12–52 (1974)Google Scholar
Copyright information
© Springer-Verlag 1991