The additive Lebesgue-type measure is spectral exactly when t1+t2 is a nonzero integer or t1-t2 is a nonzero integer; the Plus space has no exponential orthogonal basis.
Christensen, An introduction to frames and Riesz bases, Appl
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Frame bound, spectral gap and Plus space
The additive Lebesgue-type measure is spectral exactly when t1+t2 is a nonzero integer or t1-t2 is a nonzero integer; the Plus space has no exponential orthogonal basis.