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Theoretical analysis reveals a direct relationship between operators and positive operator-valued measures from Parseval frames, extending classical spectral correspondence.
Let Fₑ F e be a Parseval frame in a Hilbert space H H and let E E be a set of real numbers. From these data, we construct an operator HE,e H E , e and a positive operator-valued measure (POVM) FE,e F E , e This paper investigates in detail the relationship between the operator HE,e H E , e and the POVM FE,e F E , e . Our results extend the classical correspondence between a self-adjoint operator generated by an orthonormal basis and its associated projection-valued (spectral) measure.
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Kużel et al. (2026) studied this question.
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