An extreme absolutely continuous $\textrm {RP}$-measure
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- by John N. McDonald PDF
- Proc. Amer. Math. Soc. 109 (1990), 731-738 Request permission
Abstract:
We construct a measure on the torus ${T^2}$ which is an extreme element of the set of RP-probability measures and is absolutely continuous with respect to Haar measure on ${T^2}$.References
- Frank Forelli, A necessary condition on the extreme points of a class of holomorphic functions. II, Pacific J. Math. 92 (1981), no. 2, 277–281. MR 618065, DOI 10.2140/pjm.1981.92.277
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
- John N. McDonald, Measures on the torus which are real parts of holomorphic functions, Michigan Math. J. 29 (1982), no. 3, 259–265. MR 674279
- John N. McDonald, Examples of $\textrm {RP}$-measures, Rocky Mountain J. Math. 16 (1986), no. 1, 191–207. MR 829208, DOI 10.1216/RMJ-1986-16-1-191
- John N. McDonald, Holomorphic functions on the polydisc having positive real part, Michigan Math. J. 34 (1987), no. 1, 77–84. MR 873021, DOI 10.1307/mmj/1029003484
- Walter Rudin, Harmonic analysis in polydiscs, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 489–493. MR 0422657
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 731-738
- MSC: Primary 32A10; Secondary 30D10, 32A25
- DOI: https://doi.org/10.1090/S0002-9939-1990-1017849-0
- MathSciNet review: 1017849