The dimension of peak-interpolation sets
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- by Edgar Lee Stout
- Proc. Amer. Math. Soc. 86 (1982), 413-416
- DOI: https://doi.org/10.1090/S0002-9939-1982-0671206-0
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Abstract:
The dimension of a peak-interpolation set in the boundary of a strongly pseudoconvex domain in ${{\mathbf {C}}^N}$ does not exceed $N - 1$.References
- H. Alexander, A note on polynomial hulls, Proc. Amer. Math. Soc. 33 (1972), 389–391. MR 294689, DOI 10.1090/S0002-9939-1972-0294689-0
- Paul Alexandroff, Dimensionstheorie, Math. Ann. 106 (1932), no. 1, 161–238 (German). MR 1512756, DOI 10.1007/BF01455884
- Aldo Andreotti and Raghavan Narasimhan, A topological property of Runge pairs, Ann. of Math. (2) 76 (1962), 499–509. MR 140714, DOI 10.2307/1970370
- Errett Bishop, Holomorphic completions, analytic continuation, and the interpolation of semi-norms, Ann. of Math. (2) 78 (1963), 468–500. MR 155016, DOI 10.2307/1970537
- Th. Duchamp and E. L. Stout, Maximum modulus sets, Ann. Inst. Fourier (Grenoble) 31 (1981), no. 3, v, 37–69 (English, with French summary). MR 638616
- F. Frankl and L. Pontrjagin, Ein Knotensatz mit Anwendung auf die Dimensionstheorie, Math. Ann. 102 (1930), no. 1, 785–789 (German). MR 1512608, DOI 10.1007/BF01782377
- Felix Frankl, Charakterisierung der $n-1$-dimensionalen abgeschlossenen Mengen des $R^n$, Math. Ann. 103 (1930), no. 1, 784–787 (German). MR 1512646, DOI 10.1007/BF01455719 R. Godement, Théorie des faisceaux, Hermann, Paris, 1964. H. Hurewicz and H. Wallman, Dimension theory, Princeton Univ. Press, Princeton, N. J., 1948.
- V. I. Kuz′minov, Homological dimension theory, Uspehi Mat. Nauk 23 (1968), no. 5 (143), 3–49 (Russian). MR 0240813
- Walter Rudin, Peak-interpolation sets of class $C^{1}$, Pacific J. Math. 75 (1978), no. 1, 267–279. MR 486630 —, Function theory in the unit ball of ${{\mathbf {C}}^N}$, Springer-Verlag, New York, Heidelberg and Berlin, 1980.
- Edgar Lee Stout, The theory of uniform algebras, Bogden & Quigley, Inc., Publishers, Tarrytown-on-Hudson, N.Y., 1971. MR 0423083 A. E. Tumanov, A peak set for the disc algebra of metric dimension 2.5 in the three-dimensional unit sphere, Math. USSR Izv. 11 (1977), 353-359.
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 413-416
- MSC: Primary 32E25; Secondary 32F15
- DOI: https://doi.org/10.1090/S0002-9939-1982-0671206-0
- MathSciNet review: 671206