Abstract
We investigate here a generalized construction of spherical wavelets/needlets which admits extra-flexibility in the harmonic space, i.e., it allows the corresponding support in multipole (frequency) space to vary in more general forms than in the standard constructions. We study the analytic properties of this system and we investigate its behaviour when applied to isotropic random fields: more precisely, we establish asymptotic localization and uncorrelation properties (in the high-frequency sense) under broader assumptions than typically considered in the literature.
Funding Statement
The research by CD was supported by “Bando di Ateneo Sapienza” RM120172B7A31FFA - Costruzione di basi multiscala e trasformate wavelet per applicazioni in ambito numerico e statistico. The research by DM was partially supported by the MIUR Departments of Excellence Program Math@Tov, CUP E83C18000100006. The research by APT was partially supported by Progetto di Eccellenza, Dipartimento di Scienze Matematiche, Politecnico di Torino, CUP: E11G18000350001. APT and CD have been also partially supported by the German Research Foundation (DFG) via RTG 2131.
Citation
Claudio Durastanti. Domenico Marinucci. Anna Paola Todino. "Flexible-bandwidth needlets." Bernoulli 30 (1) 22 - 45, February 2024. https://doi.org/10.3150/22-BEJ1513
