A functional decomposition theorem for the conformal representation

Massimo LANZA DE CRISTOFORIS

doi:10.2969/jmsj/04940759

Massimo LANZA DE CRISTOFORIS

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Keywords: Conformal representation, Nonlinear operators

JOURNAL FREE ACCESS

1997 Volume 49 Issue 4 Pages 759-780

DOI https://doi.org/10.2969/jmsj/04940759

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Published: 1997 Received: June 20, 1995 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: KEYWORD Details: Right : Conformal representation, Nonlinear operators

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : Berger, M.S. (1977), Nonlinearity and Functional Analysis, Academic Press.
Coifman, R. and Meyer, V. (1983), Lavrentiev's Curves and Conformal Mappings, Institut Mittag-Leffler, Report No. 5.
Courant R. and Hilbert, D. (1962), Methods of Mathematical Physics, II, Interscience.
Gaier, D. (1964), Konstruktive Methoden der konformen Abbildung, Springer-Verlag.
Glaeser, G. (1958), Étude de quelques algèbres Tayloriennes, J. Analyse Math., 6, 1-124.
Hurewicz, W. and Wallman, H. (1948), Dimension theory, Princeton University Press.
Kantorovich, L. V. and Krylov, V.I. (1964), Approximate Methods of Higher Analysis, Interscience Publishers.
Kufner, A., John, O. and Fucik, S. (1977), Function Spaces, Noordhoff International Publishing.
Lanza de Cristoforis, M. (1991), Properties and Pathologies of the Composition and Inversion Operator in Schauder Spaces, Acc. Naz. delle Sci. detta dei XL, 15, 93-109.
Lanza de Cristoforis, M. (1992), A Note on Conformal Representation in Sobolev Spaces, Complex Variables, 20, 121-133.
Lanza de Cristoforis, M. (1993), The large deformation of nonlinearly elastic rings in a two-dimensional compressible flow, IMA Journal of Appl. Math., 50, 253-283.
Lanza de Cristoforis, M. (1994), Higher order differentiability properties of the Composition and of the Inversion Operator, Indagationes Mathematicae, New Series, 5, 457-482.
Lanza de Cristoforis, M. and Antman, S.S. (1991), The large deformation of nonlinearly elastic tubes in two-dimensional flows, SIAM J. Math. Anal., 22, 1193-1221.
Pommerenke, C. (1975), Univalent Functions, Vandenhoeck and Ruprecht, Göttingen.
Prodi, G. and Ambrosetti, A. (1973), Analisi non lineare, Editrice tecnico scientifica, Pisa.
Radó, T. (1923), Sur la représentation conforme de domaines variables, Acta Univ. Szeged., 1, 180-186.
Rohlin, V. and Fuchs, D. (1981), Premier cours de topologie-chapitres géométriques, Éditions Mir, Moscou.
Rosenblatt, A. (1936), Sur la représentation conforme de domaines plans, C.R. Acad. Sci. Paris, 202, 1398-1400.
Rosenblatt, A. (1936), Sur la représentation conforme de domains bornés limités par des courbes générales, C.R. Acad. Sci. Paris, 202, 1832-1834.
Troianiello, G.M. (1987), Elliptic Differential Equations and Obstacle Problems, Plenum Publishing Co..
Vekua, I.N. (1962), Generalized analytic functions, Pergamon Press.
Warschawski, S.E. (1935), On the Higher Derivatives at the Boundary in Conformal Mapping, Trans. Amer. Math. Soc., 38, 310-340.
Wu, S. (1993), Analytic Dependence of Riemann Mappings for Bounded Domains and Minimal Surfaces, Communications on Pure and Applied Mathematics, XLVI, 1303- 1326.
Yoshikawa, H. (1960), On the conformal mapping of nearly circular domains, J. Math. Soc. Japan, 12, 174-186.
Zeitlin, D. (1957), Behavior of conformal maps under analytic deformation of the domain, Thesis. University of Minnesota.

Right : Berger, M. S. (1977), Nonlinearity and Functional Analysis, Academic Press.
Coifman, R. and Meyer, Y. (1983), Lavrentiev's Curves and Conformal Mappings, Institut Mittag-Leffler, Report No. 5.
Courant R. and Hilbert, D. (1962), Methods of Mathematical Physics, II, Interscience.
Gaier, D. (1964), Konstruktive Methoden der konformen Abbildung, Springer-Verlag.
Glaeser, G. (1958), Étude de quelques algèbres Tayloriennes, J. Analyse Math., 6, 1-124.
Hurewicz, W. and Wallman, H. (1948), Dimension theory, Princeton University Press.
Kantorovich, L. V. and Krylov, V. I. (1964), Approximate Methods of Higher Analysis, Interscience Publishers.
Kufner, A., John, O. and Fucik, S. (1977), Function Spaces, Noordhoff International Publishing.
Lanza de Cristoforis, M. (1991), Properties and Pathologies of the Composition and Inversion Operator in Schauder Spaces, Acc. Naz. delle Sci. detta dei XL, 15, 93-109.
Lanza de Cristoforis, M. (1992), A Note on Conformal Representation in Sobolev Spaces, Complex Variables, 20, 121-133.
Lanza de Cristoforis, M. (1993), The large deformation of nonlinearly elastic rings in a two-dimensional compressible flow, IMA Journal of Appl. Math., 50, 253-283.
Lanza de Cristoforis, M. (1994), Higher order differentiability properties of the Composition and of the Inversion Operator, Indagationes Mathematicae, New Series, 5, 457-482.
Lanza de Cristoforis, M. and Antman, S. S. (1991), The large deformation of nonlinearly elastic tubes in two-dimensional flows, SIAM J. Math. Anal., 22, 1193-1221.
Pommerenke, C. (1975), Univalent Functions, Vandenhoeck and Ruprecht, Göttingen.
Prodi, G. and Ambrosetti, A. (1973), Analisi non lineare, Editrice tecnico scientifica, Pisa.
Radó, T. (1923), Sur la représentation conforme de domaines variables, Acta Univ. Szeged., 1, 180-186.
Rohlin, V. and Fuchs, D. (1981), Premier cours de topologie-chapitres géométriques, Éditions Mir, Moscou.
Rosenblatt, A. (1936), Sur la représentation conforme de domaines plans, C. R. Acad. Sci. Paris, 202, 1398-1400.
Rosenblatt, A. (1936), Sur la représentation conforme de domains bornés limités par des courbes générales, C.R. Acad. Sci. Paris, 202, 1832-1834.
Troianiello, G. M. (1987), Elliptic Differential Equations and Obstacle Problems, Plenum Publishing Co..
Vekua, I. N. (1962), Generalized analytic functions, Pergamon Press.
Warschawski, S. E. (1935), On the Higher Derivatives at the Boundary in Conformal Mapping, Trans. Amer. Math. Soc., 38, 310-340.
Wu, S. (1993), Analytic Dependence of Riemann Mappings for Bounded Domains and Minimal Surfaces, Communications on Pure and Applied Mathematics, XLVI, 1303-1326.
Yoshikawa, H. (1960), On the conformal mapping of nearly circular domains, J. Math. Soc. Japan, 12, 174-186.
Zeitlin, D. (1957), Behavior of conformal maps under analytic deformation of the domain, Thesis. University of Minnesota.

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