This book offers an overview of the research results presented by group members and guests of the Ghent Analysis & PDE Center during the weekly Ghent analysis and PDE Seminar in 20232024. It is the second book in the series of books dedicated to the seminar. The seminar is an informal event of the Analysis & PDE Center and associated researchers, where everyone can present their work or relevant literature for about 1520 minutes. The aim is to exchange ideas and foster effective learning and collaboration. In this book, group members and guests summarise their results presented during the seminar and provide outlooks for future work. In this way, the book also provides an overview of the recent developments at the Ghent Analysis & PDE Center. The main topics are functional analysis, Fourier analysis, noncommutative analysis, geometric analysis, partial differential equations of different types, harmonic analysis, functional inequalities, pseudo-differential operators, fractional derivatives, special functions, microlocal analysis, inverse problems and imaging. The target audience of this book is any researcher working in the above fields.

Provides an overview of the recent developments of the Ghent Analysis and PDE Center (20232024) Covers topics in analysis and partial differential equations Fosters effective learning and collaboration

Autorentext

Michael Ruzhansky is a senior full professor of mathematics at Ghent University in Belgium and a professor of mathematics at Queen Mary University of London in the United Kingdom.

Karel Van Bockstal is a postdoctoral researcher at the Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University.

Inhalt

Part I. Analysis.- Chapter 1. Boundedness of Toroidal Pseudo-Differential Operators on Hardy Spaces.- Chapter 2. Greedy Approximation and Universal Functions by Generalized Walsh Systems.- Chapter 3. Tables of Composition Properties of Fractional Integrals and Derivatives.- Chapter 4. Safarov Pseudo-Differential Calculus on Vector Bundles.- Chapter 5. On a Special Class of Geodesics.- Chapter 6. On Generalized Mittag-Leffler-Type Functions.- Chapter 7. Duren's Lemma for Moduli of Continuity.- Chapter 8. Frames, Theory and Applications.- Chapter 9. Some Results Related to the 𝜓-Prabhakar Fractional Derivative and the Bivariate Mittag-Leffler-Type Function.- Chapter 10. On Van der Corput-Type Estimates for Mittag-Leffler Functions.- Chapter 11. On a Sharp Vector-Valued Garding Inequality for Pseudo-Differential Operators on Compact Lie Groups.- Chapter 12. Characterization of Higher Order Fractional Weighted Homogeneous Spaces.- Chapter 13. Weak and Strong Type Estimates for Generalized Littlewood-Paley Operators.- Chapter 14. Harmonic Analysis on Twisted Crossed Products.- Part II. Partial Differential Equations.- Chapter 15. Multiplicity of solutions for a singular problem involving the 𝑝-sub-Laplacian on Stratified Lie Groups.- Chapter 16. On 𝑞2-analogue of the heat equation with spatial dependent variable coefficient.- Chapter 17. Nonlocal and Inverse Problems for a Generalized Hyperbolic-Type Equation.- Chapter 18. Analysis of Forward and Inverse Problems for the Fractional Telegraph Equation.- Chapter 19. Space-Dependent Source Identification Problem for the Subdiffusion Equation.- Chapter 20. Symbolic Differential Algorithms for the Solution of Hyperbolic Perturbation Problems by Asymptotic Formulas and Uniform Difference Schemes.- Chapter 21. Existence and Uniqueness of a Solution to the Cauchy Problem for an Equation with Singular Coefficients.- Part III. Mathematical Modelling.- Chapter 22. Unification of Newmark-Type Schemes for Fractional Oscillators.- Chapter 23. Point-Level Attribution for Interpretable Parkinson's Diagnosis.