Iterated limits in $N^{\ast } (U^{n})$
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- by Carl Stephen Davis PDF
- Trans. Amer. Math. Soc. 178 (1973), 139-146 Request permission
Abstract:
It is shown that if f is in ${N^\ast }({U^n})$, then the iterated limits of f are almost everywhere independent of the order of iteration. In fact, the iterated limit and the radial limit are equal almost everywhere.References
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- Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
- Kôsaku Yosida, Functional analysis, 2nd ed., Die Grundlehren der mathematischen Wissenschaften, Band 123, Springer-Verlag New York, Inc., New York, 1968. MR 0239384, DOI 10.1007/978-3-662-11791-0
- A. Zygmund, On the boundary values of functions of several complex variables. I, Fund. Math. 36 (1949), 207–235. MR 35832, DOI 10.4064/fm-36-1-207-235 —, Trigonometric series, 2nd ed. reprinted, Cambridge Univ. Press, New York, 1968. MR 38 #4882.
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 178 (1973), 139-146
- MSC: Primary 32A99
- DOI: https://doi.org/10.1090/S0002-9947-1973-0315155-5
- MathSciNet review: 0315155