Advances in Mathematical Physics: Methods and Applications

Dedicated to the 70th Anniversary of Ravshan Ashurov
Erscheinungsjahr 2027
ISBN: 978-3-032-42861-5
Verlag: Birkhäuser

Buch, Englisch, Format (B × H): 155 mm x 235 mm

Reihe: Research Perspectives Ghent Analysis and PDE Center

This volume is a collection of research contributions highlighting recent advances in partial differential equations, inverse and boundary value problems, spectral analysis, and fractional calculus. The book reflects current trends in mathematical analysis and mathematical physics, explores the unique solvability of inverse problems for a wide range of differential equations, and demonstrates the growing importance of fractional and nonlocal operators in the modelling of complex phenomena. By showcasing the rich interplay between inverse problems, spectral methods, and fractional differential equations, this collection offers valuable insights into emerging directions of research and serves as a useful resource for researchers, graduate students, and specialists working in these fields. The volume aims to stimulate further research, collaboration, and innovation in these dynamic areas of modern mathematics.

Zielgruppe

Research

Autoren/Hrsg.

Karimov, Erkinjon

Ruzhansky, Michael

Sobirov, Zarifboy

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

Uniform estimates for oscillatory integrals and boundedness problem for convolution operators.- The boundary-value problem for the involutory elliptic equation: well-posedness.- Weyl multiplier for convergence almost everywhere of multiple Fourier series with the
sequence of rectangular partial sums ”close to -lacunary.

Über Autor(innen)

 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. His research interests mainly lie in Partial Differential Equations, Microlocal and Harmonic Analysis, and Pseudo-Differential Operators on Lie Groups and Manifolds. Previously, he had appointments at Utrecht University, Johns Hopkins University, University of Edinburgh, and Imperial College London. He is the recipient of various awards and fellowships, notably, the Ferran Sunyer i Balaguer Prize in 2014 and 2018, Daiwa Adrian Prize in 2010, and the ISAAC award in 2007. He is serving as the head of the Ghent Analysis & PDE Center of Ghent University.

Erkinjon Karimov is a researcher at Ghent University, Belgium. His research interests include partial differential equations (PDEs), fractional calculus, and mathematical physics, with particular interests in direct and inverse problems, mixed-type equations, and fractional diffusion models. He earned his Ph.D. (2006) and D.Sc. (2020) from the V.I. Romanovskiy Institute of Mathematics of the Uzbekistan Academy of Sciences. Alongside his research activities, he is actively engaged in international collaborations, student supervision, scientific communication, and editorial work, including his role with the , promoting excellence in mathematical research and scholarship.

Zarifboy Sobirov is an associate professor (docent) at the Faculty of Mathematics of the National University of Uzbekistan in Tashkent. He received his Ph.D. in Mathematics from the same institution in 2005 and has built a distinguished career in teaching, research, and academic leadership. He has held positions at several higher education institutions, including the Tashkent Financial Institute and Chirchik State Pedagogical Institute, where he served as Head of the Department of Exact Sciences. His research focuses on direct and inverse problems for fractional differential equations on graphs, metric graph theory, fractional calculus, and models of anomalous diffusion, combining advanced analytical methods with applications to complex networked systems. In recognition of his contributions, he was awarded Uzbekistan’s Best Pedagogue-Researcher of the Year in 2015.