Nonlinear Approximation Theory in Banach Spaces

Dear Colleagues,

The theory of approximation in Banach spaces has experienced a rapid development in recent decades, driven both by its intrinsic mathematical depth and its wide range of applications in analysis, optimization, numerical mathematics, signal processing, and data science.

This Special Issue aims to bring together recent advances in nonlinear approximation theory in Banach spaces, with particular emphasis on the interplay between functional analysis, geometry of Banach spaces, and constructive approximation methods.

Potential topics include, but are not limited to, the following:

• Greedy algorithms and sparse approximation in Banach spaces.
• Norming sets, dictionaries, and bases for nonlinear approximation.
• Uniform convexity, smoothness, and geometric properties relevant to approximation.
• Adaptive methods for nonlinear approximation and applications in PDEs.
• Approximation with frames and redundant systems.
• Quantitative estimates in nonlinear approximation (Lebesgue-type inequalities, error bounds).
• Nonlinear approximation in function spaces and sequence spaces.
• Links between approximation theory, optimization, and machine learning.

Dr. Pablo M. Berná
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.