Riesz bases of exponentials for partitions of intervals

For a partition of [0, 1] with nodes 0 = a
₀
<; a
₁
<; ⋯ <; a
_n-1
<; a
_n
= 1, we construct a partition of ℤ, Λ
₁
, Λ
₂
,..., Λ
_n
such that ℰ(Λ
_j
) is a Riesz basis for L
²
[a
_j-1
, a
_j
]. Our construction also guarantees that ℰ(∪
_j=1
^k
Λ
_j
) is a Riesz basis for L
²
[0, a
_k
], and ℰ(∪
_j=k+1
ⁿ
Λ
_j
) is a Riesz basis for L
²
[a
_k
, 1].