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- W3172077962 abstract "The concept of translation of an operator allows to consider the analogue of shift-invariant subspaces in the class of Hilbert–Schmidt operators. Thus, we extend the concept of average sampling to this new setting, and we obtain the corresponding sampling formulas. The key point here is the use of the Weyl transform, a unitary mapping between the space of square integrable functions in the phase space $$mathbb {R}^dtimes widehat{mathbb {R}}^d$$ and the Hilbert space of Hilbert–Schmidt operators on $$L^2(mathbb {R}^d)$$ , which permits to take advantage of some well established sampling results." @default.
- W3172077962 created "2021-06-22" @default.
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- W3172077962 date "2021-05-27" @default.
- W3172077962 modified "2023-09-27" @default.
- W3172077962 title "Average sampling in certain subspaces of Hilbert–Schmidt operators on $$L^2(mathbb {R}^d)$$" @default.
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- W3172077962 doi "https://doi.org/10.1007/s43670-021-00011-5" @default.
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