2018/12/09 by Fethi Bouzeffour, F. Bouzeffour, Bouzeffour, F. +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Algebraic and Geometric Analysis #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #math-ph #math.FA #math.MP #math.OA
paper · pdf · doi:10.48550/arxiv.1812.03486
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openalex publication_date 2018/12/09 · arxiv created 2018/12/22 · arxiv updated 2018/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We first extend the multiplicativity property of arithmetic functions to the setting of operators on the Fock space. Secondly, we use phase operators to get representation of some extended arithmetic functions by operators on the Hardy space. Finally, we show that radial limits to the boundary of the unit disc in the Hardy space is useful in order to go back to the classical arithmetic functions. Our approach can be understudied as a transition from the classical number theory to quantum setting.