Average sampling in certain subspaces of Hilbert-Schmidt operators on\n L²(\ℝ^d)

2020/11/11 by Antonio G. Garcı́a, García, Antonio G.
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2011.05871

openalex publication_date 2020/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The concept of translation of an operator allows to consider the analogous of\nshift-invariant subspaces in the class of Hilbert-Schmidt operators. Thus, we\nextend the concept of average sampling to this new setting, and we obtain the\ncorresponding sampling formulas. The key point here is the use of the Weyl\ntransform, a unitary mapping between the space of square integrable functions\nin the phase space \ℝ^d\× widehat\ℝ^d and the Hilbert\nspace of Hilbert-Schmidt operators on L²(\ℝ^d), which permits to\ntake advantage of some well established sampling results.\n

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