Abstract
We present a method of constructing the tomographic probability distributions describing quantum states in parallel with density operators in abstract Hilbert spaces. After the study of an infinite dimensional example, the well known Husimi-Kano quasi-distribution is reconsidered in the new setting and a new tomographic scheme based on coherent states is suggested. Starting from the Sudarshan's diagonal coherent state representation, the associated identity decomposition providing Gram-Schmidt operators is explicitly given.
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