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Pseudoconvex classes of functions. III. Characterization of dual pseudoconvex classes on complex homogeneous spaces


Author: Zbigniew Slodkowski
Journal: Trans. Amer. Math. Soc. 309 (1988), 165-189
MSC: Primary 32F05; Secondary 32M10
DOI: https://doi.org/10.1090/S0002-9947-1988-0957066-9
MathSciNet review: 957066
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Abstract | References | Similar Articles | Additional Information

Abstract: Invariant classes of functions on complex homogeneous spaces, with properties similar to those of the class of plurisubharmonic functions, are studied. The main tool is a regularization method for these classes, and the main theorem characterizes dual classes of functions (where duality is defined in terms of the local maximum property). These results are crucial in proving a duality theorem for complex interpolation of normed spaces, which is given elsewhere.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1988-0957066-9
Keywords: Pseudoconvex classes, subharmonic functions, $ q$-plurisubharmonic functions, dual classes of functions, complex homogeneous spaces
Article copyright: © Copyright 1988 American Mathematical Society