February 2024 Flexible-bandwidth needlets
Claudio Durastanti, Domenico Marinucci, Anna Paola Todino
Author Affiliations +
Bernoulli 30(1): 22-45 (February 2024). DOI: 10.3150/22-BEJ1513

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

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Claudio Durastanti. Domenico Marinucci. Anna Paola Todino. "Flexible-bandwidth needlets." Bernoulli 30 (1) 22 - 45, February 2024. https://doi.org/10.3150/22-BEJ1513

Information

Received: 1 September 2021; Published: February 2024
First available in Project Euclid: 8 November 2023

MathSciNet: MR4665568
zbMATH: 07788874
Digital Object Identifier: 10.3150/22-BEJ1513

Keywords: High-frequency asymptotics , Needlets , Spherical random fields , spherical wavelets

Vol.30 • No. 1 • February 2024
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