2016/07/18 by D. R. Yafaev, Yafaev, D. R.
Computer Science · Mathematics · #47B25 #47B35 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1607.04988
openalex publication_date 2016/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We find a relation guaranteeing that Hankel operators realized in the space of sequences ℓ2 (\Bbb Z+) and in the space of functions L2 (\Bbb R+) are unitarily equivalent. This allows us to obtain exhaustive spectral results for two classes of unbounded Hankel operators in the space ℓ2 (\Bbb Z+) generalizing in different directions the classical Hilbert matrix. We also discuss a link between representations of Toeplitz operators in the spaces ℓ2 (\Bbb Z+) and L2 (\Bbb R+) .