Measures whose integral transforms are pluriharmonic

Kolaski, Clinton

doi:10.1090/S0002-9939-1979-0529217-1

Measures whose integral transforms are pluriharmonic
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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

Holomorphic functions of several compex variables with nonnegative real part. Traces of holomorphic and pluriharmonic functions on the Silov boundary

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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

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