On the Nonexistence of Certain Limits for the Complex Exponential

With {n j } an arbitrary subsequence of natural numbers, it is shown that does not exist for almost all α ∈ ℝ. The result is then applied to provide an alternative proof thatL 1(ℝ) is not weakly sequentially compact.

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Bibliographic Details
Published in:The American mathematical monthly 2013-11, Vol.120 (9), p.837-840
Main Author: Kahane, Charles S
Format: Article
Language:English
Subjects:
Integers
Mathematical functions
Mathematical lattices
Mathematical theorems
Mathematics
Natural numbers
Number theory
Polynomials
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Description
Summary:With {n j } an arbitrary subsequence of natural numbers, it is shown that does not exist for almost all α ∈ ℝ. The result is then applied to provide an alternative proof thatL 1(ℝ) is not weakly sequentially compact.
ISSN:0002-9890
1930-0972
DOI:10.4169/amer.math.monthly.120.09.837