Dynamical Representation of Frames in Tensor Product of Hardy Spaces

2023/08/22 by Nabin Kumar Sahu, Sahu, Nabin Kumar, V.S. Rajput +1 · 1 citation
Mathematics · #42C15 #46B15 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2308.11330

openalex publication_date 2023/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Dynamical Sampling of frames and tensor products are important topics in harmonic analysis. This paper combines the concepts of dynamical sampling of frames and the Carleson condition in the tensor product of Hardy spaces. Initially we discuss the preservation of the frame property under the tensor product on the Hilbert spaces. Then we discuss the iterative representation of frames in tensor product of Hardy spaces. The key ingredient of this paper is the so-called Carleson condition on the sequence \ λ_k \_k=1^∞ ⊗\ γ_l \_l=1^∞ in the open unit disc \mathbbD₁ ⊗ \mathbbD₂. Our proof is motivated by the result of Shapiro and Shields.

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• Dynamical Sampling: A Survey

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