Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An F. and M. Riesz type theorem for the unit ball in complex $ N$-space


Author: Clinton Kolaski
Journal: Proc. Amer. Math. Soc. 61 (1976), 19-25
MSC: Primary 32A30; Secondary 31B10
DOI: https://doi.org/10.1090/S0002-9939-1976-0442272-X
MathSciNet review: 0442272
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {M_B}$ denote Lebesgue measure on the open unit ball, $ B$, in complex $ N$-space and let $ M(B)$ denote the space of Borel measures on $ B$. The volume Poisson kernel $ \chi :\overline B \times B \to (0,\infty )$ is defined and then we prove Theorem. If $ \mu \in M(B)$ and if $ {\mu ^\sharp }(w) = {\smallint _B}\chi (z,w)d\mu (z)$ is pluriharmonic in $ B$, then $ {\mu ^\sharp } \in L'({M_B})$ and $ \mu = {\mu ^\sharp } \cdot {M_B}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32A30, 31B10

Retrieve articles in all journals with MSC: 32A30, 31B10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0442272-X
Keywords: Complex measure, Poisson kernel, convolution, pluriharmonic
Article copyright: © Copyright 1976 American Mathematical Society