Bohr’s power series theorem in several variables
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Publication:4356705
DOI10.1090/S0002-9939-97-04270-6zbMath0888.32001arXivmath/9606203MaRDI QIDQ4356705
Harold P. Boas, Dmitry Khavinson
Publication date: 1 October 1997
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/9606203
Power series (including lacunary series) in one complex variable (30B10) Power series, series of functions of several complex variables (32A05) Other generalizations of function theory of one complex variable (32A30)
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Cites Work
- On the absolute convergence of Dirichlet series
- On an inequality of von Neumann and an application of the metric theory of tensor products to operators theory. (Appendix by S. Kaijser and N. Th. Varopoulos.)
- Absolute bases, tensor products and a theorem of Bohr
- Sur un théorême de H. Bohr.
- The Schur multiplication in tensor algebras
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item