Measures whose integral transforms are pluriharmonic
HTML articles powered by AMS MathViewer
- by Clinton Kolaski PDF
- Proc. Amer. Math. Soc. 75 (1979), 75-80 Request permission
Abstract:
Kolaski proved an F. and M. Riesz type theorem for the unit ball in ${{\mathbf {C}}^N}$. This paper generalizes those results.References
-
L. A. Aĭzenberg and S. A. Dautov, Holomorphic functions of several compex variables with nonnegative real part. Traces of holomorphic and pluriharmonic functions on the Silov boundary, Math. USSR-Sb. 28 (1976), 301-313.
- N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337–404. MR 51437, DOI 10.1090/S0002-9947-1950-0051437-7
- Charles Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1–65. MR 350069, DOI 10.1007/BF01406845
- Frank Forelli, Measures whose Poisson integrals are pluriharmonic, Illinois J. Math. 18 (1974), 373–388. MR 342723
- Frank Forelli, Measures whose Poisson integrals are pluriharmonic. II, Illinois J. Math. 19 (1975), no. 4, 584–592. MR 477092 —, Measures whose Poisson integrals are pluriharmonic. III (to appear).
- Frank Forelli, The theorems of F. and M. Riesz for circular sets, Math. Scand. 33 (1973), 145–152. MR 341101, DOI 10.7146/math.scand.a-11480
- Frank Forelli and Walter Rudin, Projections on spaces of holomorphic functions in balls, Indiana Univ. Math. J. 24 (1974/75), 593–602. MR 357866, DOI 10.1512/iumj.1974.24.24044
- Lars Hörmander, An introduction to complex analysis in several variables, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0203075
- Clinton J. Kolaski, A new look at a theorem of Forelli and Rudin, Indiana Univ. Math. J. 28 (1979), no. 3, 495–499. MR 529680, DOI 10.1512/iumj.1979.28.28034
- Clinton Kolaski, An F. and M. Riesz type theorem for the unit ball in complex $N$-space, Proc. Amer. Math. Soc. 61 (1976), no. 1, 19–25 (1977). MR 442272, DOI 10.1090/S0002-9939-1976-0442272-X
- Leopoldo Nachbin, Holomorphic functions, domains of holomorphy and local properties, North-Holland Mathematics Studies, vol. 1, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1970. Notes prepared by Richard M. Aron. MR 0274798
- Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 75 (1979), 75-80
- MSC: Primary 32A35; Secondary 31C10, 32F05
- DOI: https://doi.org/10.1090/S0002-9939-1979-0529217-1
- MathSciNet review: 529217