科研之友
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摘要
Let. be a symmetric measure of Lebesgue type, i.e., @@@ rho = 1/2 (mu X delta(0) + delta(0) x mu), @@@ where the component measure mu is the Lebesguemeasure supported on [t, t + 1] for t is an element of Q\{- 1/2} and delta(0) is the Dirac measure at 0. We prove that rho is a spectral measure if and only if t is an element of 1/2Z. In this case, L-2(rho) has a unique orthonormal basis of the form @@@ {e(2 pi i(lambda x-lambda y)) : lambda is an element of Lambda(0) }, @@@ where Lambda(0) is the spectrum of the Lebesgue measure supported on [-t - 1,-t]boolean OR[t, t + 1]. Our result answers some questions raised by Lai, Liu and Prince [ JFA, 2021].
