@article{AIHPC_1986__3_1_67_0, author = {Fliess, Michel}, title = {Vers une notion de d\'erivation fonctionnelle causale}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {3}, year = {1986}, pages = {67-76}, mrnumber = {837731}, zbl = {0602.93032}, language = {fr}, url = {http://dml.mathdoc.fr/item/AIHPC_1986__3_1_67_0} }
Fliess, Michel. Vers une notion de dérivation fonctionnelle causale. Annales de l'I.H.P. Analyse non linéaire, Tome 3 (1986) pp. 67-76. http://gdmltest.u-ga.fr/item/AIHPC_1986__3_1_67_0/
[1] The use of functionals in the analysis of non-linear physical systems, J. Electronics Control, t. 15, 1963, p. 567-615.
,[2] Les séries rationnelles et leurs langages, Masson, Paris, 1984. | MR 745968 | Zbl 0573.68037
et ,[3] | MR 274237 | Zbl 0211.02401
, Algèbre I (chap. 1 à 3), Hermann, Paris, 1970.[4] Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula, Ann. of Math., t. 65, 1957, p. 163-178. | MR 85251 | Zbl 0077.25301
,[5] Algebraic paths, J. Algebra, t. 10, 1968, p. 8-36. | MR 229630 | Zbl 0204.33803
,[6] Iterated path integrals, Bull. Amer. Math. Soc., t. 83, 1977, p. 831-879. | MR 454968 | Zbl 0389.58001
,[7] Creep and Relaxation of Nonlinear Visco-elastic Materials, North-Holland, Amsterdam, 1976. | MR 431847 | Zbl 0345.73034
, et ,[8] Fonctionnelles causales non linéaires et indéterminées non commutatives, Bull. Soc. Math. France, t. 109, 1981, p. 3-40. | Numdam | MR 613847 | Zbl 0476.93021
,[9] Réalisation locale des systèmes non linéaires, algèbres de Lie filtrées transitives et series génératrices non commutatives, Inventiones Math., t. 71, 1983, p. 521-537. | MR 695904 | Zbl 0513.93014
,[10] On the concept of derivatives and Taylor expansions for nonlinear input-output systems, Proc. 22nd IEEE Conf. Decision Control, p. 643-646, San Antonio, TX, 1983.
,[11] An algebraic approach to nonlinear functional expansions, IEEE Trans. Circuits Systems, t. 30, 1983, p. 554-570. | MR 715510 | Zbl 0529.34002
, et ,[12] Application of a new functional expansion to the cubic anharmonic oscillator, J. Math. Physics, t. 23, 1982, p. 495-502. | MR 649526
et ,[13] Algèbres de Lie nilpotentes, formule de Baker-Campbell-Hausdorff et intégrales itérées de K. T. Chen, Séminaire de Probabilités XVI 1980/1981, J. Azéma et M. Yor eds., p. 257-267, Lect. Notes Math. 920, Springer-Verlag, Berlin, 1982. | Numdam | MR 658689 | Zbl 0495.60064
et ,[14] Die symbolische Exponentialformel in der Gruppentheorie, Leipziger Ber., t. 58, 1906, p. 19-48. | JFM 37.0176.02
,[15] Combinatorial Group Theory, Interscience, New York, 1966.
, et ,[16] Actions of formal groups on formal schemes. Application to control theory and combinatorics, Séminaire M.-P. Malliavin, Paris, 1983. | Zbl 0617.14029
,[17] Lie elements and an algebra associated with shuffles, Ann. of Math., t. 68, 1958, p. 210-220. | MR 100011 | Zbl 0083.25401
,[18] An Introduction to Combinatorial Analysis, Wiley, New York, 1958. | MR 96594 | Zbl 0078.00805
,[19] Formulations of Classical and Quantum Dynamical Theory, Academic Press, New York, 1969. | MR 273906 | Zbl 0195.28102
,[20] A cyclic derivative in noncommutative algebra, J. Algebra, t. 64, 1980, p. 54-75. | MR 575782 | Zbl 0428.16036
, et ,[21] Nonlinear System Theory, The Johns Hopkins University Press, Baltimore, 1981. | MR 713994 | Zbl 0666.93065
,[22] Field Theory, t. 2, Polish Scientific Publishers, Varsovie, et, Iliffe Books, Londres, 1969.
,[23] The Volterra and Wiener Theories of Nonlinear Systems, Wiley, New York, 1980. | MR 562917 | Zbl 0501.93002
,[24] Die Anfänge der Funktionalanalysis und ihr Platz im Umwälzungsprozess der Mathematik um 1900, Arch. History Exact Sc., t. 26, 1982, p. 13-71. | MR 664469 | Zbl 0514.46001
,[25] Hopf Algebras, Benjamin, New York, 1968. | MR 252485 | Zbl 0194.32901
,[26] Leçons sur les fonctions de lignes, Gauthier-Villars, Paris, 1913.
,[27] Théorie générale des fonctionnelles, t. 1, Gauthier-Villars, Paris. 1936. | JFM 62.0455.01 | Zbl 0015.30501
et ,