Nous étudions les sous-ensembles du bord d’un domaine strictement pseudoconvexe
We investigate some aspects of maximum modulus sets in the boundary of a strictly pseudoconvex domain
@article{AIF_1981__31_3_37_0, author = {Duchamp, Thomas and Stout, Edgar Lee}, title = {Maximum modulus sets}, journal = {Annales de l'Institut Fourier}, pages = {37--69}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {31}, number = {3}, year = {1981}, doi = {10.5802/aif.837}, mrnumber = {83d:32019}, zbl = {0439.32007}, language = {en}, url = {https://www.numdam.org/articles/10.5802/aif.837/} }
TY - JOUR AU - Duchamp, Thomas AU - Stout, Edgar Lee TI - Maximum modulus sets JO - Annales de l'Institut Fourier PY - 1981 SP - 37 EP - 69 VL - 31 IS - 3 PB - Institut Fourier PP - Grenoble UR - https://www.numdam.org/articles/10.5802/aif.837/ DO - 10.5802/aif.837 LA - en ID - AIF_1981__31_3_37_0 ER -
Duchamp, Thomas; Stout, Edgar Lee. Maximum modulus sets. Annales de l'Institut Fourier, Tome 31 (1981) no. 3, pp. 37-69. doi : 10.5802/aif.837. https://www.numdam.org/articles/10.5802/aif.837/
[1] Polynomial approximation and hulls in sets of finite linear measure in Cn, Amer. J. Math., 93 (1971), 65-74. | MR | Zbl
,[2] A topological property of Runge pairs, Ann. Math., (2) 76 (1962), 499-509. | MR | Zbl
and ,[3] A generalization of the Stone-Weierstrass theorem, Pacific J. Math., 11 (1961), 777-783. | MR | Zbl
,[4] Contact Manifolds in Riemannian Geometry, Springer Lecture Notes in Mathematics, vol. 509, Springer-Verlag, Berlin, Heidelberg, New York, 1976. | MR | Zbl
,[5] Cohomology of maximal ideal spaces, Bull. Amer. Math. Soc., 67 (1961), 515-516. | MR | Zbl
,[6] Extending functions from submanifolds of the boundary, Duke Math., J., 43 (1976), 391-404. | MR | Zbl
and ,[7] Variétés analytiques réelles et variétés analytiques complexes, Bull. Soc. Math. France, 85 (1957), 77-99. | Numdam | MR | Zbl
,[8] Ensembles pics pour A∞ (D), Ann. Inst. Fourier, Grenoble, XXIX (1979), 171-200. | Numdam | MR | Zbl
and ,[9] Peak interpolation sets for some algebras of analytic functions, Pacific J. Math., 41 (1972), 81-87. | MR | Zbl
and ,[10] Geometric Measure Theory, Springer-Verlag New York, Inc., New York, 1969. | MR | Zbl
,[11] The classification of Legendre embeddings, to appear.
,[12] Embedding strictly pseudoconvex domains in convex domains, Amer. J. Math., 98 (1976), 529-569. | MR | Zbl
,[13] Analytic Functions of Several Complex Variables, Prentice-Hall, Englewood Cliffs, 1965. | MR | Zbl
and ,[14] Families of analytic discs in Cn with boundaries on a prescribed CR submanifold, Ann. Scuola Norm. Sup. Pisa Sci., (IV) V, (1978), 327-380. | Numdam | MR | Zbl
and ,[15] Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, 1962. | MR | Zbl
,[16] Dimension Theory, Princeton University Press, Princeton, 1948. | Zbl
and ,[17] Behavior of Holomorphic Functions at Generating Submanifolds of the Boundary, doctoral dissertation, University of Washington, Seattle, 1979.
,[18] Lectures on the Quantitative Theory of Foliations, CBMS Regional Conference Series in Mathematics, Number 27, American Mathematical Society, Providence, Rhode Island, 1977. | Zbl
,[19] Advanced Calculus, Addison-Wesley, Reading, 1968. | MR | Zbl
and ,[20] Topology from the Differentiable Viewpoint, University Press of Virginia, Charlottesville, 1965. | MR | Zbl
,[21] Geometrisch Untersuchungen allgemeiner und einiger spezieller Pseudokonvexer Gebiete, Bonner Math. Schriften, 78, Bonn, 1975. | Zbl
,[22] A boundary uniqueness theorem for holomorphic functions of several complex variables, Math. Notes, 15 (1974), 116-120. | MR | Zbl
,
[23] Ck approximation by holomorphic functions and
[24] Sur certaines propriétés topologiques des variétés feuilletées, Act. Sci. Indust., 1183, Hermann, Paris, 1952. | MR | Zbl
,[25] Peak interpolation manifolds of class C1, Pacific J. Math., 75 (1978), 267-279. | MR | Zbl
,[26] Lectures on the Edge-of-the-Wedge Theorem, CBMS Regional Conference Series in Mathematics, Number 6, American Mathematical Society, Providence, Rhode Island, 1971. | MR | Zbl
,[27] Boundary properties of functions of several complex variables, J. Math. Mech., 14 (1965), 991-1006. | MR | Zbl
and ,[28] A boundary uniqueness theorem in Cn, Math. USSR Sbornik, 30 (1976), 501-514. | Zbl
,[29] Nonlinear Functional Analysis, Gordon and Breach, New York, 1969. | MR | Zbl
,[30] On the continuation of analytic curves, Math. Ann., 184 (1970), 268-274. | MR | Zbl
,[31] Valeurs au bord de fonctions holomorphes et ensembles polynomialement convexes, Séminaire Pierre Lelong 1975-1976. Springer Lecture Notes in Mathematics, vol. 578, Springer-Verlag, Berlin, Heidelberg, New York, 1977. | Zbl
,[32] Analytische Projektion komplexer Mannigfaltigkeiten, Colloque sur les Fonctions de Plusieurs Variables, Brussels, 1953. George Throne, Leige and Masson, Paris, 1953. | Zbl
,[32a] Die Existenz Komplexer Basen zu holomorphen Abbildungen, Math. Ann., 136 (1958), 1-8. | MR | Zbl
,[33] Lectures on Differential Geometry, Prentice-Hall, Englewood Cliffs, 1964. | MR | Zbl
,[34] The Theory of Uniform Algebras, Bogden and Quigley, Tarrytown-on-Hudson and Belmont, 1971. | MR | Zbl
,[35] Interpolation manifolds, Recent Developments in Several Complex Variables, Annals of Mathematics Studies, to appear. | Zbl
,[36] A peak set for the disc algebra of metric dimension 2.5 in the three-dimensional unit sphere, Math. USSR Izvestija, 11 (1977), 370-377. | MR | Zbl
,[37] Zero-sets of continuous holomorphic functions on the boundary of a strongly pseudoconvex domain, J. London Math. Soc., 18 (1978), 484-488. | MR | Zbl
,[38] Compact real submanifolds of a complex manifold with nondegenerate holomorphic tangent bundles, Math. Ann., 179 (1969), 123-129. | MR | Zbl
,[39] Real analytic subvarieties and holomorphic approximation, Math. Ann., 179 (1969), 130-141. | MR | Zbl
,[40] Trigonometric Series, vol. I., Cambridge University Press, Cambridge, 1959. | Zbl
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boundary, Complex Analysis and Operator Theory, Volume 17 (2023) no. 2 | DOI:10.1007/s11785-022-01321-9 - The convergence of hulls of curves, Mathematische Zeitschrift, Volume 301 (2022) no. 3, p. 3071 | DOI:10.1007/s00209-022-02972-2
- Manifold-Valued Holomorphic Approximation, Canadian Mathematical Bulletin, Volume 54 (2011) no. 2, p. 370 | DOI:10.4153/cmb-2010-103-5
- Rationally convex sets on the unit sphere in ℂ2, Arkiv för Matematik, Volume 46 (2008) no. 1, p. 183 | DOI:10.1007/s11512-007-0055-8
- Characterisation of homogeneous polynomials which are constant on complex-tangential curves in the boundary of the unit ball of, Mathematische Annalen, Volume 335 (2006) no. 4, p. 737 | DOI:10.1007/s00208-005-0712-9
- Maximum Modulus Sets and Segre Convexity, Mathematische Nachrichten, Volume 230 (2001) no. 1, p. 37 | DOI:10.1002/1522-2616(200110)230:1<37::aid-mana37>3.0.co;2-l
- Finite Interpolation with Minimum Uniform Norm in Cn, Journal of Functional Analysis, Volume 170 (2000) no. 2, p. 512 | DOI:10.1006/jfan.1999.3509
- On complex-tangential curves on the unit sphere on
and homogeneous polynomials, Proceedings of the Japan Academy, Series A, Mathematical Sciences, Volume 76 (2000) no. 3 | DOI:10.3792/pjaa.76.39 - CR functions vanishing on open sets (almost) complex structures and Cohen's example, Indagationes Mathematicae, Volume 9 (1998) no. 2, p. 289 | DOI:10.1016/s0019-3577(98)80025-6
- Function Theory in the Ball, Several Complex Variables II, Volume 8 (1994), p. 107 | DOI:10.1007/978-3-642-57882-3_3
- A reflection principle on strongly pseudoconvex domains with generic corners, Mathematische Zeitschrift, Volume 213 (1993) no. 1, p. 49 | DOI:10.1007/bf03025708
- Maximum modulus sets in pseudoconvex boundaries, Journal of Geometric Analysis, Volume 2 (1992) no. 4, p. 327 | DOI:10.1007/bf02934585
- Local Peak Sets and Maximum Modulus Sets in Products of Strictly Pseudoconvex Domains, Complex Analysis, Volume 1 (1991), p. 155 | DOI:10.1007/978-3-322-86856-5_25
- A characterization of totally real generic submanifolds of strictly pseudoconvex boundaries in ? n admitting a local foliation by interpolation submanifolds, Mathematische Annalen, Volume 288 (1990) no. 1, p. 505 | DOI:10.1007/bf01444544
- A characterization of weak pseudoconvexity, Proceedings of the American Mathematical Society, Volume 105 (1989) no. 2, p. 314 | DOI:10.1090/s0002-9939-1989-0933520-7
- Interpolation theory in Cn: A suryey, Complex Analysis, Volume 1268 (1987), p. 158 | DOI:10.1007/bfb0097302
- Interpolation manifolds for products of strictly pseudoconvex domains, Complex Variables, Theory and Application: An International Journal, Volume 8 (1987) no. 3-4, p. 333 | DOI:10.1080/17476938708814242
- Dimension de Hausdorff des ensembles de zéros et d’interpolation pour 𝐴^∞(𝐷), Transactions of the American Mathematical Society, Volume 299 (1987) no. 1, p. 95 | DOI:10.1090/s0002-9947-1987-0869401-x
- Dense morphisms in commutative Banach algebras, Transactions of the American Mathematical Society, Volume 304 (1987) no. 2, p. 537 | DOI:10.1090/s0002-9947-1987-0911084-4
- On the behavior of holomorphic functions near maximum modulus sets, Mathematische Annalen, Volume 276 (1986) no. 1, p. 137 | DOI:10.1007/bf01450930
- The dimension of peak-interpolation sets, Proceedings of the American Mathematical Society, Volume 86 (1982) no. 3, p. 413 | DOI:10.1090/s0002-9939-1982-0671206-0
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