An Application of the supremum cosine angle between multiplication invariant spaces in L²(X; \mc H)

2022/11/28 by Sudipta Sarkar, Sarkar, Sudipta, Sahil Kalra +3
Engineering · Mathematics · #42C40 #43A32 #43A65 #47A15 #94A20 #Advanced Harmonic Analysis Research #Advanced Numerical Analysis Techniques #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2211.15238

openalex publication_date 2022/11/28 · openalex created_date 2022/12/10 · openalex updated_date 2026/07/28

Abstract

In this article, we describe the supremum cosine angle between two multiplication invariant (MI) spaces and its connection with the closedness of the sum of those spaces. The results obtained for MI spaces are preserved by the corresponding fiber spaces almost everywhere. Employing the Zak transform, we obtain the results for translation invariant spaces on locally compact groups by action of its closed abelian subgroup. Additionally, we provide the application of our results to sampling theory.

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