Duván Cardona

5. Subelliptic Pseudo-differential operators and Fourier integral operators on compact Lie groups

Published in: MSJ Memoirs: Memoirs of the Mathematical Society of Japan

Cited as: Cardona, D., Ruzhansky, M. Subelliptic pseudo-differential operators and Fourier integral operators on compact Lie groups.
MSJ Memoirs, Math. Soc. Japan, 44: 175pp. (2025). arXiv:2008.09651.
Arxiv Link
Project Euclid Link
Math. Soc. Japan link

Fields: Analysis and PDE.

Authors: Duván Cardona and Michael Ruzhansky

Overview:

In this memoir we extend the theory of global pseudo-differential operators to the setting of arbitrary sub-Riemannian structures on a compact Lie group. More precisely, given a compact Lie group and the sub-Laplacian associated to a system of vector fields satisfying the Hormander condition, we introduce a subelliptic pseudo-differential calculus associated to the operator L, based on the matrix-valued quantisation process developed in reference one hundred thirty-eight. This theory will be developed as follows. First, we investigate the singular kernels of this calculus, estimates of Lp to Lp, H1 to L1, Linfinity to BMO type, and also the weak one-one boundedness of these subelliptic Hormander classes. Among the obtained estimates we prove subelliptic versions of the celebrated sharp Fefferman Lp theorem and the Calderon-Vaillancourt theorem.

4. Book: Analysis and PDE in Developing Countries

Published in: Research Perspectives Ghent Analysis and PDE Center, Springer-Birkhäuser.

Cited as: Cardona, D., Kähler, U. (eds) Analysis and PDE in developing Countries. Proceedings of the ISAAC-ICMAM Conference 2024. Trends in Mathematics, vol 17. Birkhäuser, Cham, 2026.

Fields: Analysis and PDE.

Editors: Duván Cardona and Uwe Kähler

Springer Link

The current volume collects selected contributions from the ISAAC–ICMAM Conference of Analysis in Developing Countries 2024, organised jointly by the International Society for Analysis, its Applications and Computation (ISAAC) and the International Community of Mathematicians from Latin America (ICMAM Latin America). Topics covered include microlocal analysis, spectral theory, Clifford and hypercomplex analysis, pseudo-differential and Fourier integral operators, harmonic analysis over non-commutative structures, PDE on nilpotent Lie groups, fractional diffusion models, conservation laws, and dispersive equations. This book will be of interest to researchers working in these topics.

3. Book: Analysis and PDE in Latin America

Published in: Research Perspectives Ghent Analysis and PDE Center, Springer-Birkhäuser.

Cited as: Cardona, D., Grajales, B. (eds) Analysis and PDE in Latin America. ICMAM 2023-2024. Trends in Mathematics, vol 15. Birkhäuser, Cham, 2025.

Fields: Analysis and PDE.

Editors: Duván Cardona and Brian Grajales

Springer Link

This book is the third in a series of books dedicated to publishing extended abstracts of the activities of ICMAM Latin America (International Community of Mathematicians from Latin America). This book includes selected contributions of speakers at the ICMAM Latin America Satellite Conference on Analysis and PDE 2023. This book is a comprehensive collection of the latest advancements in the fields of Analysis and Partial Differential Equations (PDE) in Latin America.

This book is an essential resource for mathematicians, researchers, and students interested in the latest developments in Analysis and PDE.

2. Book: Analysis and PDE in Latin America

Published in: Research Perspectives Ghent Analysis and PDE Center, Springer-Birkhäuser.

Cited as: Cardona, D., Grajales, B. (eds) Analysis and PDE in Latin America. ICMAM 2022. Trends in Mathematics, vol 10. Birkhäuser, Cham, 2024.

Fields: Analysis and PDE.

Editors: Duván Cardona and Brian Grajales;

Springer Link

This book presents the extended abstracts of the 2022 International Conference: Multidisciplinary Aspects in Mathematics and its applications (ICMAM) Latin America conference. The book presents the current state of the art in Analysis and PDEs in Latin America. Topics include: PDE models describing epidemics, population dynamics, climatological risks, oil prospection, impedance tomography in the detection of medical diseases, and abstract theory of PDEs. The extended abstracts presented in this book includes contributions by several renowned mathematicians in analysis and PDEs.

List of Authors and Articles in this Book

1. Book: Extended Abstracts 2021/2022 Methusalem Lectures

Published in: Research Perspectives Ghent Analysis and PDE Center, Springer-Birkhäuser.

Cited as: Cardona, D., Restrepo, J., Ruzhansky, M. (Editors). Extended Abstracts 2021/2022, Methusalem Lectures, Research Perspectives: Ghent Analysis and PDE Center, Trends in Mathematics. Birkhäuser, 2023.

Fields: Geometric Analysis and PDE.

Editors: Duván Cardona, Joel Restrepo, and Michael Ruzhansky;

Springer Link

This volume presents modern developments in analysis, PDEs and geometric analysis by some of the leading worldwide experts, prominent junior and senior researchers who were invited to be part of the Ghent Analysis & PDE Center Methusalem Seminars from 2021 to 2022. The contributions are from the speakers of the Methusalem Colloquium, Methusalem Junior Seminar and Geometric Analysis Seminar.