{e±i(n−1/4)t}n∈N Is Not a Basis of L2[−π,π]

In connection with showing that Kadec′s 14 constant is best possible, the example of {e±i(n−1/4)t}n∈N as an exact sequence arises, whence {1, e±i(n−1/4)t}n∈N cannot be a Riesz basis. The question of whether {e±i(n−1/4)t}n∈N is a basis is resolved in this paper. This problem was brought to our attention by R. M. Young ("An Introduction to Nonharmonic Fourier Series, p. 223, Academic Press, New York/London,1980).