Asymptotically holomorphic functions and translation invariant subspaces of weighted Hilbert spaces of sequences
Esterle, Jean ; Volberg, Alexander
Annales scientifiques de l'École Normale Supérieure, Tome 35 (2002), p. 185-230 / Harvested from Numdam
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@article{ASENS_2002_4_35_2_185_0,
     author = {Esterle, Jean and Volberg, Alexander},
     title = {Asymptotically holomorphic functions and translation invariant subspaces of weighted Hilbert spaces of sequences},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {35},
     year = {2002},
     pages = {185-230},
     doi = {10.1016/s0012-9593(02)01088-1},
     mrnumber = {1914931},
     zbl = {1059.47034},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_2002_4_35_2_185_0}
}

Esterle, Jean; Volberg, Alexander. Asymptotically holomorphic functions and translation invariant subspaces of weighted Hilbert spaces of sequences. Annales scientifiques de l'École Normale Supérieure, Tome 35 (2002) pp. 185-230. doi : 10.1016/s0012-9593(02)01088-1. http://gdmltest.u-ga.fr/item/ASENS_2002_4_35_2_185_0/

[1] Abkar A., Hedenmalm H., Invariant subspaces on multiply connected domains, Publ. Math. 42 (1998) 521-557. | MR 1676042 | Zbl 0927.47002

[2] Aleman A., Richter S., Ross W.T., Pseudocontinuations and the Backward Shift, Indiana Math. J. 47 (1) (1998) 223-276. | MR 1631561 | Zbl 0907.46019

[3] Aleman A., Richter S., Sundberg C., Beurling's theorem for the Bergman space, Acta Math. 177 (1996) 275-310. | MR 1440934 | Zbl 0886.30026

[4] Apostol C., Hyperinvariant subspaces for bilateral weighted shifts, J. Int. Eq. Op. Theory 7 (1984) 1-9. | MR 802365 | Zbl 0574.47005

[5] Atzmon A., An operator without invariant subspace on a nuclear Fréchet space, Ann. of Math. 117 (1983) 660-694. | MR 701260 | Zbl 0553.47002

[6] Atzmon A., An operator on a Fréchet space with no common invariant subspace with its inverse, J. Funct. Anal. 55 (1984) 68-77. | MR 733034 | Zbl 0552.47006

[7] Atzmon A., Nuclear Fréchet spaces of entire functions with transitive differentiation, J. Analyse Math. 60 (1993) 1-19. | MR 1253226 | Zbl 0801.46004

[8] Atzmon A., Entire functions, invariant subspaces and Fourier transforms, Israel Math. Conference Proceedings 11 (1997) 37-52. | MR 1476702 | Zbl 0907.30029

[9] Atzmon A., Weighted Lp spaces of entire functions, Fourier transforms and invariant subspaces, Preprint.

[10] Atzmon A., The existence of self-adjoint translation invariant subspaces on symmetric self-adjoint sequence spaces on Z, J. Funct. Anal. 178 (2000) 372-380. | MR 1802899 | Zbl 0978.47022

[11] Atzmon A., Sodin M., Completely indecomposable operators and a uniqueness theorem of Cartwright-Levinson type, J. Funct. Anal. 169 (1999) 164-188. | MR 1726751 | Zbl 0945.47012

[12] Beurling A., Mittag-Leffler lectures in Complex Analysis (1977-78); Collected works of A. Beurling, 361-443.

[13] Beurling A., Malliavin P., On Fourier transforms of measures with compact support, Acta Math. 107 (1962) 291-309. | MR 147848 | Zbl 0127.32601

[14] Borichev A., Boundary uniqueness theorems for almost analytic functions, and asymmetric algebras of sequences, Math. USSR Sb. 64 (2) (1989) 323-338. | MR 959485 | Zbl 0677.30003

[15] Borichev A., Invariant subspaces of given index in Banach spaces of analytic functions, J. Reine Angew. Math. 505 (1998) 23-44. | MR 1662236 | Zbl 0923.47003

[16] Borichev A., Hedenmalm H., Completeness of translates in weighted spaces on the half-line, Acta Math. 174 (1995) 1-84. | MR 1310845 | Zbl 0830.46020

[17] Borichev A., Hedenmalm H., Volberg A., Large Bergman spaces: invertibility, cyclicity, and subspaces of arbitrary index, Preprint. | MR 2027638

[18] Borichev A., Volberg A., Uniqueness theorems for almost analytic functions, Leningrad Math. J. 1 (1990) 157-190. | MR 1015338 | Zbl 0725.30038

[19] Bourgain J., A problem of Douglas and Rudin of factorization, Pacific J. Math. 121 (1) (1986) 47-50. | MR 815031 | Zbl 0609.30035

[20] Brown S., Chevreau B., Pearcy C., On the structure of contraction operators II, J. Funct. Anal. 76 (1988) 269-293. | MR 923043 | Zbl 0641.47013

[21] Domar Y., Translation invariant subspaces of weighted ℓp and Lp spaces, Math. Scand. 49 (1981) 133-144. | MR 645094 | Zbl 0465.47020

[22] Domar Y., Entire functions of order ≤1, with bounds on both axes, Ann. Acad. Sci. Fenn. 22 (1997) 339-348. | Zbl 0913.30017

[23] Dynkin E.M., Functions with a given estimate for ∂f/∂z ¯ and N. Levinson's theorem, Math. Sb. 81 (1972) 182-190. | Zbl 0263.30027

[24] El Fallah O., Kellay K., Sous-espaces biinvariants pour certains shifts à poids, Ann. Inst. Fourier 48 (1998) 1543-1588. | Numdam | MR 1662275 | Zbl 0919.47020

[25] Esterle J., Singular inner functions and biinvariants subspaces for dissymmetric weighted shifts, J. Funct. Anal. 44 (1997) 64-104. | MR 1430716 | Zbl 0938.47003

[26] Esterle J., Countable inductive limits of Fréchet algebras, J. Ann. Math. 71 (1997) 195-204. | MR 1454251 | Zbl 0905.46032

[27] Esterle J., Exact factorization never holds for Banach spaces of sequences, St. Petersburg Math. J. 12 (2001) 869-874. | MR 1812948 | Zbl 1013.46016

[28] Esterle J., Apostol's bilateral weighted shifts are hyperreflexive, Operator Theory: Advances and Applications 127 (2001) 243-266. | MR 1902804 | Zbl 0994.47009

[29] Esterle J., Gay R., Product of hyperfunctions on the circle, Israel J. Math. 116 (2000) 271-283. | MR 1759409 | Zbl 0964.32005

[30] Esterle J., Volberg A., Sous-espaces invariants par translation de certains espaces de Hilbert de suites quasi-analytiquement pondérées, C. R. Acad. Sci. Paris, Ser. A 326 (1998) 295-300. | MR 1648437 | Zbl 0919.47009

[31] Esterle J., Volberg A., Analytic left-invariant subspaces of weighted Hilbert spaces of sequences, J. Op. Theory 45 (2001) 265-301. | MR 1841097 | Zbl 1002.47001

[32] Harlouchet I., Trace de Cauchy pour certaines fonctions localement intégrables sur un ouvert borné de C, submitted. | Zbl 02074330

[33] Harlouchet I., Idéaux fermés de certaines algèbres de Beurling quasi-analytiques sur le cercle unité, J. Math. Pures Appl. 79 (2000) 863-899. | MR 1792728 | Zbl 1040.30028

[34] Hedenmalm H., A comparison between the closed modular ideals of ℓ1(ω) and L1(ω), Math. Scand. 58 (1986) 275-300. | Zbl 0654.46056

[35] Hedenmalm H., Bounded analytic functions and closed ideals, J. Anal. Math. 48 (1987) 142-166. | MR 910006 | Zbl 0633.46055

[36] Hedenmalm H., Korenblum B., Zhu K., The Theory of Bergman Spaces, GTM 199, Springer-Verlag, 2000. | MR 1758653 | Zbl 0955.32003

[37] Hedenmalm H., Volberg A., Zero-free invariant subspaces in weighted Bergman spaces with critical topology, Preprint.

[38] Helson H., Lectures on Invariant Subspaces, Academic Press, 1954. | MR 171178 | Zbl 0119.11303

[39] Hitt D., Invariant subspaces of H2 of an annulus, Pacific J. Math. 134 (1) (1988) 101-120. | MR 953502 | Zbl 0662.30035

[40] Kellay K., Fonctions intérieures et vecteurs bicycliques, Archiv. der Math. 77 (2001) 253-264. | MR 1865867 | Zbl 1021.47005

[41] Korenblum B., Outer functions and cyclic elements in Bergman spaces, J. Funct. Anal. 115 (1993) 104-118. | MR 1228143 | Zbl 0780.30028

[42] Matsaev V.I., Mogulskii E.Z., A division theorem for analytic functions with a given majorant and some of its applications, J. Soviet Math. 14 (1980) 1078-1091. | Zbl 0442.30050

[43] Nikolskii N., Selected problems in weighted approximations and spectral analysis, Proc. Steklov Inst. Math. 120 (1974). | Zbl 0342.41028

[44] Nikolskii N., Treatise on the Shift Operator, Springer-Verlag, Berlin, 1986. | MR 827223 | Zbl 0587.47036

[45] Nikolskii N., Yngve Domar's forty years in harmonic analysis, Festschrift in honour of Lennart Carleson and Yngve Domar (Uppsala, 1993), Acta Univ. Upsaliensis 58 (1995) 45-78. | MR 1351999 | Zbl 0845.43001

[46] Sarason D., The Hp-spaces of an annulus, Mem. Amer. Math. Soc. 56 (1965). | MR 188824 | Zbl 0127.07002

[47] Sarason D., Nearly invariant subspaces for the backward shift, Operator Theory Adv. Appl. 35 (1988) 481-493. | MR 1017680 | Zbl 0687.47003

[48] Shields A., Weighted shift operators and analytic function theory, in: Pearcy C. (Ed.), Topics in Operator Theory, Amer. Math. Soc. Math. Surveys, 13, 1974, pp. 49-128. | MR 361899 | Zbl 0303.47021

[49] Volberg A., The logarithm of an almost analytic function is summable, Soviet Math. Dokl. 26 (1982) 238-243. | Zbl 0518.30034

[50] Volberg A., Asymptotically holomorphic functions and certain of their applications, Proc. I.C.M. Kyoto II (1990) 959-967. | MR 1159281 | Zbl 0744.30038

[51] Volberg A., Joricke B., Summability of the logarithm of an almost analytic function and a generalization of the Levinson-Cartwright theorem, Math. USSR Sb. 58 (1987) 337-349. | Zbl 0644.30020

[52] Wiener N., Tauberian theorems, Ann. of Math. 33 (1932) 1-100. | JFM 58.0226.02 | MR 1503035

[53] Yakubovitch D., Invariant subspaces of the operator of multiplication by z in the space Ep in a multiply connected domain, LOMI, Stek. Akad. Nauk. SSSR 178 (1989) 166-183. | MR 1037771 | Zbl 0722.47031