A Sequence of Fourier Partial Sums not Containing 2¼Q
Abstract
In this paper, we focus on the bounded sequences of Fourier
partial sums. Our interest is on the sequences which do not contain any
rational multiple of 2¼. We construct a function on C[T] where its set of
points is one of such sequences. We will show that this set is of the first
category in R. Moreover the complement of this set in any arbitrary
real closed interval form an uncountable set.
partial sums. Our interest is on the sequences which do not contain any
rational multiple of 2¼. We construct a function on C[T] where its set of
points is one of such sequences. We will show that this set is of the first
category in R. Moreover the complement of this set in any arbitrary
real closed interval form an uncountable set.
Keywords
Fourier partial sums, trigonometric series,
Fourier coefficients
Refbacks
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution 3.0 License.