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Volumn , Issue 780, 2003, Pages

Quasianalytic monogenic solutions of a cohomological equation

Author keywords

Borel's monogenic functions; Carleman classes; Continued fractions; Hadamard's product; Resurgence theory; Small divisors

Indexed keywords


EID: 85087247167     PISSN: 00659266     EISSN: None     Source Type: Journal    
DOI: 10.1090/memo/0780     Document Type: Article
Times cited : (15)

References (53)
  • 1
    • 0038594115 scopus 로고
    • On the Whitney's extension theorem
    • [ALG]
    • [ALG] J.-C. Archer and E. Le Gruyer, "On the Whitney's extension theorem," Bull. Sci. Math. 119 (1995), 235-266.
    • (1995) Bull. Sci. Math. , vol.119 , pp. 235-266
    • Archer, J.-C.1    Le Gruyer, E.2
  • 2
    • 0000071902 scopus 로고
    • On the mappings of the circumference onto itself
    • [Ar], 2nd series
    • [Ar] V. I. Arnold, "On the mappings of the circumference onto itself," Translations of the Amer. Math. Soc. 46 (1961), 2nd series, 213-284.
    • (1961) Translations of the Amer. Math. Soc. , vol.46 , pp. 213-284
    • Arnold, V.I.1
  • 4
    • 0034412187 scopus 로고    scopus 로고
    • Limit at resonances of linearizations of some complex analytic dynamical systems
    • [BMS]
    • [BMS] A. Berretti, S. Marmi and D. Sauzin, "Limit at resonances of linearizations of some complex analytic dynamical systems," Ergodic Theory and Dynamical Systems 20 (2000), 963-990.
    • (2000) Ergodic Theory and Dynamical Systems , vol.20 , pp. 963-990
    • Berretti, A.1    Marmi, S.2    Sauzin, D.3
  • 5
    • 84903754385 scopus 로고
    • Sur les fonctions limites quasi-analytiques des fractions rationelles
    • [Be1], Stockholm
    • [Be1] A. Beurling, "Sur les fonctions limites quasi-analytiques des fractions rationelles," 8th Scandinavian Math. Congress, Stockholm (1934), 199-210; in Collected Works of Arne Beurling, Birkhäuser, Boston Basel Berlin, Vol. I (1989), 109-120.
    • (1934) 8th Scandinavian Math. Congress , pp. 199-210
    • Beurling, A.1
  • 6
    • 0037917952 scopus 로고
    • Birkhäuser, Boston Basel Berlin
    • [Be1] A. Beurling, "Sur les fonctions limites quasi-analytiques des fractions rationelles," 8th Scandinavian Math. Congress, Stockholm (1934), 199-210; in Collected Works of Arne Beurling, Birkhäuser, Boston Basel Berlin, Vol. I (1989), 109-120.
    • (1989) Collected Works of Arne Beurling , vol.1 , pp. 109-120
  • 7
    • 0005678301 scopus 로고
    • On quasianalyticity and general distributions
    • [Be2], Summer School, Stanford University
    • [Be2] A. Beurling, "On quasianalyticity and general distributions," Multilithed Lecture Notes, Summer School, Stanford University (1961); in Collected Works of Arne Beurling, Birkhäuser, Boston Basel Berlin, Vol. I (1989), 309-338.
    • (1961) Multilithed Lecture Notes
    • Beurling, A.1
  • 8
    • 0038594119 scopus 로고
    • Birkhäuser, Boston Basel Berlin
    • [Be2] A. Beurling, "On quasianalyticity and general distributions," Multilithed Lecture Notes, Summer School, Stanford University (1961); in Collected Works of Arne Beurling, Birkhäuser, Boston Basel Berlin, Vol. I (1989), 309-338.
    • (1989) Collected Works of Arne Beurling , vol.1 , pp. 309-338
  • 13
    • 0037579938 scopus 로고
    • Sur les séries de fractions rationelles
    • [De]
    • [De] A. Denjoy, "Sur les séries de fractions rationelles," Bull. de la Soc. Math. de France 52 (1924), 418-434.
    • (1924) Bull. de la Soc. Math. de France , vol.52 , pp. 418-434
    • Denjoy, A.1
  • 14
    • 0030637332 scopus 로고    scopus 로고
    • Explicit computation of Padé-Hermite approximants
    • [Du]
    • [Du] D. Duverney, "Explicit computation of Padé-Hermite approximants," J. Approx. Th. 88 (1997), 80-91.
    • (1997) J. Approx. Th. , vol.88 , pp. 80-91
    • Duverney, D.1
  • 15
    • 4243681588 scopus 로고
    • Les fonctions résurgentes et leurs applications
    • [E1], 05, vol. II: 81-06, 05
    • [E1] J. Écalle, Les fonctions résurgentes et leurs applications, Publ. math. d'Orsay, vol. I: 81-05, vol. II: 81-06, vol. III: 85-05 (1981, 1985).
    • (1981) Publ. Math. d'Orsay , vol.1-3 , Issue.81-85
    • Écalle, J.1
  • 16
    • 0002204718 scopus 로고
    • Singularités non abordables par la géométrie
    • [E2]
    • [E2] J. Écalle, "Singularités non abordables par la géométrie," Ann. Inst. Fourier, Grenoble 42 (1992), 73-194.
    • (1992) Ann. Inst. Fourier, Grenoble , vol.42 , pp. 73-194
    • Écalle, J.1
  • 18
    • 0004277259 scopus 로고
    • [Ga], Prentice-Hall, Engelwood Cliffs
    • [Ga] T. W. Gamelin, Uniform Algebras, Prentice-Hall, Engelwood Cliffs (1969).
    • (1969) Uniform Algebras
    • Gamelin, T.W.1
  • 19
    • 0038255567 scopus 로고
    • Continuation of functions beyond natural boundaries
    • [Gam]
    • [Gam] J. L. Gammel, "Continuation of functions beyond natural boundaries," Rocky Mountain J. Math. 4 (1974), 203-206.
    • (1974) Rocky Mountain J. Math. , vol.4 , pp. 203-206
    • Gammel, J.L.1
  • 20
    • 0038255566 scopus 로고
    • Convergence of Padé approximants to quasianalytic functions beyond natural boundaries
    • [GN]
    • [GN] J. L. Gammel and J. Nuttall, "Convergence of Padé Approximants to quasianalytic functions beyond natural boundaries," J. Math. Analys. Appl. 43 (1973), 694-696.
    • (1973) J. Math. Analys. Appl. , vol.43 , pp. 694-696
    • Gammel, J.L.1    Nuttall, J.2
  • 21
    • 51249169934 scopus 로고
    • Étude de quelques algèbres tayloriennes
    • [Gl]
    • [Gl] G. Glaeser, "Étude de quelques algèbres tayloriennes," J. Anal Math. Jerusalem 6 (1958), 1-124.
    • (1958) J. Anal Math. Jerusalem , vol.6 , pp. 1-124
    • Glaeser, G.1
  • 22
    • 0038594120 scopus 로고
    • Sur les fonctions à espaces lacunaires
    • [Gou]
    • [Gou] E. Goursat, "Sur les fonctions à espaces lacunaires," Bull. Sci. Math. 11 (1887), 109-114.
    • (1887) Bull. Sci. Math. , vol.11 , pp. 109-114
    • Goursat, E.1
  • 23
    • 0002159192 scopus 로고
    • Notes on the theory of series (XXIV): A curious power-series
    • [HL]
    • [HL] G. H. Hardy and J. E. Littlewood, "Notes on the theory of series (XXIV): a curious power-series," Proc. Cambridge Phil. Soc. 42 (1946), 85-88.
    • (1946) Proc. Cambridge Phil. Soc. , vol.42 , pp. 85-88
    • Hardy, G.H.1    Littlewood, J.E.2
  • 25
    • 51249179424 scopus 로고
    • Simple proofs of local conjugacy theorems for diffeomorphisms of the circle with almost every rotation numbers
    • [He]
    • [He] M. R. Herman, "Simple proofs of local conjugacy theorems for diffeomorphisms of the circle with almost every rotation numbers," Bull. Soc. Bras. Mat. 16 (1985), 45-83.
    • (1985) Bull. Soc. Bras. Mat. , vol.16 , pp. 45-83
    • Herman, M.R.1
  • 26
    • 0003918560 scopus 로고
    • [Khi], The University of Chicago Press, Chicago London
    • [Khi] A. Ya. Khinchin, Continued Fractions, The University of Chicago Press, Chicago London (1964).
    • (1964) Continued Fractions
    • Khinchin, A.Ya.1
  • 27
    • 0001441814 scopus 로고    scopus 로고
    • The general theory of dynamical systems and classical mechanics
    • [Ko], Amsterdam
    • [Ko] A. N. Kolmogorov, "The General Theory of Dynamical Systems and Classical Mechanics", address to the 1954 International Congress of Mathematicians, Amsterdam.
    • 1954 International Congress of Mathematicians
    • Kolmogorov, A.N.1
  • 28
    • 0003352579 scopus 로고
    • Elliptic functions
    • [La], Springer-Verlag
    • [La] S. Lang, Elliptic functions, Graduate Texts in Math. 112, Springer-Verlag (1987).
    • (1987) Graduate Texts in Math. , vol.112
    • Lang, S.1
  • 29
    • 0000651275 scopus 로고
    • Sommation des séries divergentes
    • [Ma]
    • [Ma] B. Malgrange, "Sommation des séries divergentes," Expos. Math. 13 (1995), 163-222.
    • (1995) Expos. Math. , vol.13 , pp. 163-222
    • Malgrange, B.1
  • 30
    • 0031548111 scopus 로고    scopus 로고
    • The Brjuno functions and their regularity properties
    • [MMY]
    • [MMY] S. Marmi, P. Moussa and J.-C. Yoccoz, "The Brjuno functions and their regularity properties," Comm. Math. Phys. 186 (1997), 265-293.
    • (1997) Comm. Math. Phys. , vol.186 , pp. 265-293
    • Marmi, S.1    Moussa, P.2    Yoccoz, J.-C.3
  • 31
    • 0037917955 scopus 로고
    • The Hadamard multiplication theorem and applications in summability theory
    • [Mü]
    • [Mü] J. Müller, "The Hadamard Multiplication Theorem and Applications in Summability Theory," Complex Variables 18 (1992), 155-166.
    • (1992) Complex Variables , vol.18 , pp. 155-166
    • Müller, J.1
  • 32
    • 0010761294 scopus 로고
    • Sur les fonctions à espaces lacunaires
    • [P1]
    • [P1] H. Poincaré, "Sur les fonctions à espaces lacunaires," Amer. J. Math. 14 (1892), 201-221.
    • (1892) Amer. J. Math. , vol.14 , pp. 201-221
    • Poincaré, H.1
  • 33
    • 0037579950 scopus 로고
    • Analyse de ses travaux sur la théorie générale des fonctions d'une variable
    • [P2]
    • [P2] H. Poincaré, "Analyse de ses travaux sur la théorie générale des fonctions d'une variable," Acta Math. 38 (1921), 65-70.
    • (1921) Acta Math. , vol.38 , pp. 65-70
    • Poincaré, H.1
  • 34
    • 84990623105 scopus 로고
    • Integrability of Hamiltonian systems on Cantor sets
    • [Pö]
    • [Pö] J. Pöschel, "Integrability of Hamiltonian systems on Cantor sets," Comm. Pure Appl. Math. 35 (1982), 653-696.
    • (1982) Comm. Pure Appl. Math. , vol.35 , pp. 653-696
    • Pöschel, J.1
  • 35
    • 12144267827 scopus 로고
    • Séries divergentes et théories asymptotiques
    • [Ra], Panoramas et synthèses
    • [Ra] J.-P. Ramis, Séries divergentes et théories asymptotiques, Panoramas et synthèses, Suppl. au Bull. de la Soc. Math. de France 121 (1993).
    • (1993) Suppl. au Bull. de la Soc. Math. de France , vol.121
    • Ramis, J.-P.1
  • 36
    • 0003206321 scopus 로고    scopus 로고
    • Classical topics in complex function theory
    • [Re], Springer-Verlag
    • [Re] R. Remmert, Classical Topics in Complex Function Theory, Graduate Texts in Math. 172, Springer-Verlag (1998).
    • (1998) Graduate Texts in Math. , vol.172
    • Remmert, R.1
  • 37
    • 0013238434 scopus 로고    scopus 로고
    • Linéarisation des perturbations holomorphes des rotations et applications
    • [Ris]
    • [Ris] E. Risler, Linéarisation des perturbations holomorphes des rotations et applications, Mémoires de la Soc. Math, de France 77 (1999).
    • (1999) Mémoires de la Soc. Math, de France , vol.77
    • Risler, E.1
  • 38
    • 84979310133 scopus 로고
    • Der Hadamardsche multiplicationssatz und weitere kompositions sätze der funktionentheorie
    • [Sc]
    • [Sc] S. Schottlaender, "Der Hadamardsche Multiplicationssatz und weitere Kompositions sätze der Funktionentheorie," Math. Nachr. 11 (1954), 239-294.
    • (1954) Math. Nachr. , vol.11 , pp. 239-294
    • Schottlaender, S.1
  • 39
    • 0038255564 scopus 로고    scopus 로고
    • Uniqueness theorems for Wolff-Denjoy series
    • [Si]
    • [Si] R. V. Sibiliev, "Uniqueness theorems for Wolff-Denjoy series," St. Petersburg Math. J. 7 (1996), 145-168.
    • (1996) St. Petersburg Math. J. , vol.7 , pp. 145-168
    • Sibiliev, R.V.1
  • 40
    • 0000553786 scopus 로고
    • Almost periodic Schrodinger operators IV. The Maryland model
    • [Sim]
    • [Sim] B. Simon, "Almost periodic Schrodinger operators IV. The Maryland model," Ann. Phys. 159 (1985), 157-183.
    • (1985) Ann. Phys. , vol.159 , pp. 157-183
    • Simon, B.1
  • 41
    • 0003201639 scopus 로고
    • Singular integrals and differentiability properties of functions
    • [St]
    • [St] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Math. Series 30 (1970).
    • (1970) Princeton Math. Series , vol.30
    • Stein, E.M.1
  • 42
    • 0038594121 scopus 로고    scopus 로고
    • Quelques propriétés de quasi-analyticité
    • [Th]
    • [Th] V. Thilliez, "Quelques propriétés de quasi-analyticité," Gazette des Mathematiciens 70 (1996), 49-68.
    • (1996) Gazette des Mathematiciens , vol.70 , pp. 49-68
    • Thilliez, V.1
  • 44
    • 0038594133 scopus 로고
    • On quasi-analytic functions
    • [Tj]
    • [Tj] W. J. Trjitzinsky, "On Quasi-Analytic Functions," Ann. of Math. 30 (1930), 526-546.
    • (1930) Ann. of Math. , vol.30 , pp. 526-546
    • Trjitzinsky, W.J.1
  • 46
    • 77956456169 scopus 로고
    • Analytic extensions of differentiable functions defined in closed sets
    • [Wh]
    • [Wh] H. Whitney, "Analytic extensions of differentiable functions defined in closed sets," Trans. Amer. Math. Soc. 36 (1934), 63-89.
    • (1934) Trans. Amer. Math. Soc. , vol.36 , pp. 63-89
    • Whitney, H.1
  • 47
    • 0038594126 scopus 로고
    • A uniqueness theorem for monogenic functions
    • [Wk]
    • [Wk] J. Winkler, "A uniqueness theorem for monogenic functions," Ann. Acad. Sci. Fennicae Ser. A. I. Math. 18 (1993), 105-116.
    • (1993) Ann. Acad. Sci. Fennicae Ser. A. I. Math. , vol.18 , pp. 105-116
    • Winkler, J.1
  • 48
    • 0037579955 scopus 로고
    • The linear difference equation of first order for angular variables
    • [Wi]
    • [Wi] A. Wintner, "The linear difference equation of first order for angular variables," Duke Math. J. 12 (1945), 445-449.
    • (1945) Duke Math. J. , vol.12 , pp. 445-449
    • Wintner, A.1
  • 51
    • 0002419165 scopus 로고
    • Petits diviseurs en dimension un
    • [Y2]
    • [Y2] J.-C. Yoccoz, "Petits diviseurs en dimension un," Astérisque 231 (1995).
    • (1995) Astérisque , vol.231
    • Yoccoz, J.-C.1
  • 52
    • 0037579941 scopus 로고    scopus 로고
    • Analytic linearization of analytic circle diffeomorphisms
    • [Y3], lectures given at the CIME school "Dynamical Systems and Small Divisors", Cetraro (Italy)
    • [Y3] J.-C. Yoccoz, "Analytic linearization of analytic circle diffeomorphisms," lectures given at the CIME school "Dynamical Systems and Small Divisors", Cetraro (Italy) 1998, to appear in the CIME series of Lecture Notes in Math.
    • (1998) CIME Series of Lecture Notes in Math.
    • Yoccoz, J.-C.1
  • 53
    • 0003293139 scopus 로고
    • Analytic capacity and rational approximation
    • [Za], Springer
    • [Za] L. Zalcman, Analytic capacity and rational approximation, Lecture Notes in Math. 50, Springer (1968).
    • (1968) Lecture Notes in Math. , vol.50
    • Zalcman, L.1


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