New Perspectives in Harmonic Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 651

Special Issue Editor


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Guest Editor
Department of Mathematics and Statistics, American University, Washington, DC, USA
Interests: complex analysis; harmonic analysis; differential geometry; number theory with applications to signal and image processing

Special Issue Information

Dear Colleagues,

This Special Issue of Mathematics, entitled New Perspectives in Harmonic Analysis, aims to present recent advances in harmonic analysis and to explore new trends and directions in related areas. We therefore welcome papers that address a range of topics including, but not limited to,  signal and image processing, compressed sensing, coding theory, control theory computational neuroscience, deep learning, information theory, and theoretical, applied, and computational harmonic analysis.

Prof. Dr. Stephen Casey
Guest Editor

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Keywords

  • shannon sampling
  • irregular sampling
  • interpolation theory
  • Gabor systems
  • wavelets
  • frame theory
  • information theory
  • deep learning

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Published Papers (1 paper)

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Research

22 pages, 266 KiB  
Article
Spectral Theory and Hardy Spaces for Bessel Operators in Non-Standard Geometries
by Saeed Hashemi Sababe
Mathematics 2025, 13(4), 565; https://doi.org/10.3390/math13040565 - 8 Feb 2025
Viewed by 457
Abstract
This paper develops novel results in the harmonic analysis of Bessel operators, extending their theory to higher-dimensional and non-Euclidean spaces. We present a refined framework for Hardy spaces associated with Bessel operators, emphasizing atomic decompositions, dual spaces, and connections to Sobolev and Besov [...] Read more.
This paper develops novel results in the harmonic analysis of Bessel operators, extending their theory to higher-dimensional and non-Euclidean spaces. We present a refined framework for Hardy spaces associated with Bessel operators, emphasizing atomic decompositions, dual spaces, and connections to Sobolev and Besov spaces. The spectral theory of families of boundary-interpolating operators is also expanded, offering precise eigenvalue estimates and functional calculus applications. Furthermore, we explore Bessel operators under non-standard measures, such as fractal and weighted geometries, uncovering new analytical phenomena. Key implications include advanced insights into singular integrals, heat kernel behavior, and the boundedness of Riesz transforms, with potential applications in fractal geometry, constrained wave propagation, and mathematical physics. Full article
(This article belongs to the Special Issue New Perspectives in Harmonic Analysis)
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