Research in Mathematics

Harmonic Analysis: Theory, Computation, and Applications

Harmonic analysis has evolved into a prominent branch of modern mathematics, offering unique and powerful frameworks for analysing functions through their spectral and structural properties. Though the field of harmonic analysis primarily emerged from Fourier analysis, it has gradually transformed into a broader discipline within the context of mathematical analysis subsuming the field of Fourier Analysis. The field now encompasses a broad spectrum of theoretical, computational, and application-driven developments in pure and applied mathematics. For instance, time-frequency analysis, wavelet theory, representation theory, pseudo-differential operators and Fourier integral operators, and inverse problems are all studied under the roof of harmonic analysis. In addition to this, the field has also resulted in numerous other pursuits of knowledge, including abstract harmonic analysis, harmonic analysis on graphs, and applications of harmonic analysis in quantum mechanics, data science and machine learning. This Article Collection aims to bring together strong contributions across different verticals of harmonic analysis spanning foundational theory, numerical methods, and impactful applications.

Particularly, the theme of this Article Collection is to gather a collection of articles reflecting the latest theoretical and empirical developments within the realm of applied and computational harmonic analysis. This Article Collection is also aimed to provide a multidisciplinary forum to mathematicians, scientists and engineers working on different aspects of pure and applied harmonic analysis, to promote these methods in diverse research areas.

The importance of harmonic analysis lies in its ability to provide rigorous mathematical frameworks for understanding complex phenomena arising in both natural and engineering sciences. Many modern technologies—including medical imaging, wireless communications, audio and image processing, quantum information, and machine learning—rely fundamentally on harmonic analytic methods for efficient representation, reconstruction, and interpretation of data. At the theoretical level, harmonic analysis also plays a crucial role in partial differential equations, spectral theory, and mathematical physics, offering tools to study regularity, stability, and propagation phenomena. Computational developments such as wavelets, sparse approximation, and compressed sensing have transformed the way high-dimensional data are processed and analysed. Furthermore, the increasing interaction between harmonic analysis and emerging engineering fields has opened new research directions with substantial societal and scientific impact. An Article Collection on this theme is therefore timely and valuable for consolidating recent progress and encouraging interdisciplinary collaboration across mathematics, computation, and applications.

This Article Collection welcomes review, expository, and original research articles closely related to the theme of the issue. Potential topics include but are not limited to the following:

• Theoretical Harmonic Analysis
• Time-Frequency and Phase-Space Analysis
• Harmonic Analysis and PDEs
• Computational Harmonic Analysis
• Harmonic Analysis in Inverse Problems
• Harmonic Analysis on Groups and Geometric Structures
• Emerging Directions and Interdisciplinary Connections
• Spectral and Potential Theory
• Scattering Theory
• Applications

Keywords: Harmonic Analysis, Time-Frequency and Phase-Space Analysis, Fourier and Wavelet Theory, Signal and Image Processing, Inverse Problems

Manuscript Submissions:

Manuscript submission is open until 31st March 2027.

Please carefully review the journal scope and author submission instructions prior to submitting a manuscript as it will be rejected if it does not fall within the scope of the journal.

All manuscripts submitted to this Article Collection will undergo desk assessment and peer-review as part of our standard editorial process. Manuscripts which do not fall within the scope of the journal will be rejected.

We are able to offer a 10% Discount to all authors, and have a limited number of 20% Discount codes only available for early submissions. It should be noted that discount codes must be entered in at the point of submission as they cannot be applied retroactively, nor can these be combined as only the higher valued discount would be applicable.

To submit your papers to this Article Collection, please:

1. Check "Yes" for the question, "Are you submitting your paper for a specific special issue or article collection?"
2. Select the relevant Article Collection from the drop-down menu under the question, "Harmonic Analysis: Theory, Computation, and Applications"
3. Enter the Discount Code on the Final Page (Services) in the “Apply Discount Code” box on the right-hand side of the screen, otherwise this will not be applied to your submission, and you could be then subject to the journal’s Full APC Fee

Please contact Christopher Montgomery, Commissioning Editor regarding details on obtaining your discount codes, and with any other queries for this Article Collection.

Article Collection Guest Advisors

Prof. Firdous A. Shah obtained his bachelor’s and master’s degrees from the Department of Mathematics at the University of Kashmir and a PhD in Mathematics at the Central University, Jamia Millia Islamia, New Delhi, India. Currently, he is an Associate Professor of Mathematics at the University of Kashmir, India. He has authored and co-authored numerous (over 200) research articles in mathematical analysis and applied harmonic analysis. Besides, he has co-authored and edited several research books in wavelet analysis and time-frequency methods with major international publishers, including Springer, Taylor & Francis, and Academic Press. He is also serving as an editorial board member of several mathematics and engineering journals and a reviewer of several international journals. His current citation count is 3859 (Google Scholar) with an h-index of 28 and an i10-index of 87. He has undertaken several research projects, and already 12 students have completed their Ph.D research work under his guidance. His current research interests include the development of new time-frequency transforms, multi-scale wavelet analysis, applied harmonic analysis, Clifford Fourier transforms, and their applications to differential and integral equations, signal processing, and mathematical biology.

Prof. Hatem Mejjaoli of the Department of Mathematics, College of Sciences, Taibah University, Al Madinah Al Munawarah, Saudi Arabia. His research interests lie mainly in harmonic analysis, time-frequency analysis, Dunkl theory, wavelet transforms, generalized Fourier analysis, and uncertainty principles. He has published over 210 research articles in international mathematical journals and has made significant contributions to generalized transforms, spectral analysis, and functional analysis.

Dr Azhar Yousuf has a PhD in Mathematics with specialization in Wavelets. His research interests broadly lie within Applied Harmonic Analysis, and he is particularly interested in Signal Processing. His most recent works are in the fields of Compressed sensing: Theoretical bounds, algorithms, applications, and Signal representation.