2023/12/28 by Junjie Miao, Hongbo Zhao, Miao, Junjie +1 · 1 citation
Mathematics · #42A85 #42C05 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2312.16863
openalex publication_date 2023/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the spectrality of infinite convolutions generated by infinitely many admissible pairs which may not be compactly supported, where the spectrality means the corresponding square integrable function space admits a family of exponential functions as an orthonormal basis. First, we prove that the infinite convolution exists and is a spectral measure if the sequence of admissible pairs satisfies the remainder bounded condition, and it has a subsequence consisting of general consecutive sets. Then we show that the subsequence of general consecutive sets may be replaced by a general assumption, named θ-bounded condition. Finally, we investigate the infinite convolutions generated by special subsequences, and give a sufficient condition for the spectrality of such infinite convolutions.