Spectrality of Infinite Convolutions and Random Convolutions

Abstract

In this paper, we explore spectral measures whose square integrable spaces admit a family of exponential functions as an orthonormal basis.Our approach involves utilizing the integral periodic zeros set of Fourier transform to characterize spectrality of infinite convolutions generated by a sequence of admissible pairs.Then we delve into the analysis of the integral periodic zeros set. Finally, we show that given finitely many admissible pairs, almost all random convolutions are spectral measures. Moreover, we give a complete characterization of spectrality of random convolutions in some special cases.

31 pages, final version

References in corpus (4)

• Complex Hadamard matrices and the Spectral Set Conjecture
• On Fuglede's conjecture and the existence of universal spectra
• Spectrality of random convolutions generated by finitely many Hadamard triples
• The divergence of Mock Fourier series for spectral measures