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This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudodifferential operators, partial differential equations, and timefrequency analysis. It is based on lectures given at the international conference "Fourier Analysis and PseudoDifferential Operators," June 2530, 2012, at Aalto University, Finland. This collection of 20 refereed articles is based on selected talks and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series "Fourier Analysis and Partial Differential Equations."

Nonlinear Analysis: Problems, Applications and Computational Methods
Michael Ruzhansky, Hemen Dutta, Said Melliani, Zakia Hammouch
 Springer
 13 Novembre 2020
 9783030622992
This book is a collection of original research papers as proceedings of the 6th International Congress of the Moroccan Society of Applied Mathematics organized by Sultan Moulay Slimane University, Morocco, during 7th9th November 2019. It focuses on new problems, applications and computational methods in the field of nonlinear analysis. It includes various topics including fractional differential systems of various types, timefractional systems, nonlinear Jerk equations, reproducing kernel Hilbert space method, thrombin receptor activation mechanism model, labour force evolution model, nonsmooth vector optimization problems, anisotropic elliptic nonlinear problem, viscous primitive equations of geophysics, quadratic optimal control problem, multiorthogonal projections and generalized continued fractions.
The conference aimed at fostering cooperation among students, researchers and experts from diverse areas of applied mathematics and related sciences through fruitful deliberations on new research findings. This book is expected to be resourceful for researchers, educators and graduate students interested in applied mathematics and interactions of mathematics with other branches of science and engineering.

Functional Analysis in Interdisciplinary Applications
Tynysbek Sh. Kalmenov, Erlan D. Nursultanov, Michael V. Ruzhansky, Tynysbek Sh. Sadybekov
 Springer
 12 Décembre 2017
 9783319670539
This volume presents current research in functional analysis and its applications to a variety of problems in mathematics and mathematical physics. The book contains over forty carefully refereed contributions to the conference "Functional Analysis in Interdisciplinary Applications" (Astana, Kazakhstan, October 2017). Topics covered include the theory of functions and functional spaces; differential equations and boundary value problems; the relationship between differential equations, integral operators and spectral theory; and mathematical methods in physical sciences. Presenting a wide range of topics and results, this book will appeal to anyone working in the subject area, including researchers and students interested to learn more about different aspects and applications of functional analysis.

Quantization on Nilpotent Lie Groups
Michael Ruzhansky, Veronique Fischer
 Birkhäuser
 8 Mars 2016
 9783319295589
This book presents a consistent development of the KohnNirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups.
The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize. 
Advances in Real and Complex Analysis with Applications
Yeol Je Cho, Michael Ruzhansky, Praveen Agarwal, Michael Area
 Birkhäuser
 3 Octobre 2017
 9789811043376
This book discusses a variety of topics in mathematics and engineering as well as their applications, clearly explaining the mathematical concepts in the simplest possible way and illustrating them with a number of solved examples. The topics include real and complex analysis, special functions and analytic number theory, qseries, Ramanujan's mathematics, fractional calculus, Clifford and harmonic analysis, graph theory, complex analysis, complex dynamical systems, complex function spaces and operator theory, geometric analysis of complex manifolds, geometric function theory, Riemannian surfaces, Teichmüller spaces and Kleinian groups, engineering applications of complex analytic methods, nonlinear analysis, inequality theory, potential theory, partial differential equations, numerical analysis , fixedpoint theory, variational inequality, equilibrium problems, optimization problems, stability of functional equations, and mathematical physics. It includes papers presented at the 24th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (24ICFIDCAA), held at the Anand International College of Engineering, Jaipur, 2226 August 2016. The book is a valuable resource for researchers in real and complex analysis.

Methods of Fourier Analysis and Approximation Theory
Michael Ruzhansky, Sergey Tikhonov
 Birkhäuser
 11 Mars 2016
 9783319274669
Different facets of interplay between harmonic analysis and
approximation theory are covered in this volume. The topics included are
Fourier analysis, function spaces, optimization theory, partial differential
equations, and their links to modern developments in the approximation theory.
The articles of this collection were originated from two events. The first event
took place during the 9th ISAAC Congress in Krakow, Poland, 5th9th August
2013, at the section "Approximation
Theory and Fourier Analysis". The second
event was the conference on Fourier Analysis and Approximation Theory in the
Centre de Recerca Matemàtica (CRM), Barcelona, during 4th8th November 2013,
organized by the editors of this volume. All articles selected to be part of
this collection were carefully reviewed. 
Mathematical Analysis and Applications
Ravi P. Agarwal, Michael Ruzhansky, Hemen Dutta
 Wiley
 11 Avril 2018
 9781119414339
An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, manybody wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and FussCatalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authorsa noted team of international researchers in the field highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a widerange of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

Analysis and Partial Differential Equations: Perspectives from Developing Countries
Michael Ruzhansky, Julio Delgado
 Springer
 27 Janvier 2019
 9783030056575
This volume presents current trends in analysis and partial differential equations from researchers in developing countries. The fruit of the project 'Analysis in Developing Countries', whose aim was to bring together researchers from around the world, the volume also includes some contributions from researchers from developed countries.Focusing on topics in analysis related to partial differential equations, this volume contains selected contributions from the activities of the project at Imperial College London, namely the conference on Analysis and Partial Differential Equations held in September 2016 and the subsequent Official Development Assistance Week held in November 2016. Topics represented include Fourier analysis, pseudodifferential operators, integral equations, as well as related topics from numerical analysis and bifurcation theory, and the countries represented range from Burkina Faso and Ghana to Armenia, Kyrgyzstan and Tajikistan, including contributions from Brazil, Colombia and Cuba, as well as India and China.Suitable for postgraduate students and beyond, this volume offers the reader a broader, global perspective of contemporary research in analysis.

Analytic Methods in Interdisciplinary Applications
Michael Ruzhansky, Vladimir V. Mityushev
 Springer
 20 Novembre 2014
 9783319121482
The book includes lectures given by the plenary and key speakers at the 9th International ISAAC Congress held 2013 in Krakow, Poland. The contributions treat recent developments in analysis and surrounding areas, concerning topics from the theory of partial differential equations, function spaces, scattering, probability theory, and others, as well as applications to biomathematics, queueing models, fractured porous media and geomechanics.

Progress in Partial Differential Equations
Michael Reissig, Michael Ruzhansky
 Springer
 30 Mars 2013
 9783319001258
Progress in Partial Differential Equations is devoted to modern topics in the theory of partial differential equations. It consists of both original articles and survey papers covering a wide scope of research topics in partial differential equations and their applications. The contributors were participants of the 8th ISAAC congress in Moscow in 2011 or are members of the PDE interest group of the ISAAC society.This volume is addressed to graduate students at various levels as well as researchers in partial differential equations and related fields. The readers will find this an excellent resource of both introductory and advanced material. The key topics are:o Linear hyperbolic equations and systems (scattering, symmetrisers)
o Nonlinear wave models (global existence, decay estimates, blowup)
o Evolution equations (control theory, wellposedness, smoothing)
o Elliptic equations (uniqueness, nonuniqueness, positive solutions)
o Special models from applications (Kirchhoff equation, ZakharovKuznetsov equation, thermoelasticity) 
Hardy Inequalities on Homogeneous Groups
Michael Ruzhansky, Durvudkhan Suragan
 Birkhäuser
 2 Juillet 2019
 9783030028954
This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, CaffarelliKohnNirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of subLaplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hrmander's sums of squares and their fundamental solutions.
This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding. 
Current Trends in Analysis and Its Applications
Michael V. Ruzhansky, Vladimir V. Mityushev
 Birkhäuser
 4 Février 2015
 9783319125770
This book is a collection of papers from the 9th International ISAAC Congress held in 2013 in Kraków, Poland. The papers are devoted to recent results in mathematics, focused on analysis and a wide range of its applications. These include uptodate findings of the following topics: Differential Equations: Complex and Functional Analytic Methods Nonlinear PDE Qualitative Properties of Evolution Models Differential and Difference Equations Toeplitz Operators Wavelet Theory Topological and Geometrical Methods of Analysis Queueing Theory and Performance Evaluation of Computer Networks Clifford and Quaternion Analysis Fixed Point Theory MFrame Constructions Spaces of Differentiable Functions of Several Real VariablesGeneralized Functions Analytic Methods in Complex Geometry Topological and Geometrical Methods of Analysis Integral Transforms and Reproducing Kernels Didactical Approaches to Mathematical ThinkingTheir wide applications in biomathematics, mechanics, queueing models, scattering, geomechanics etc. are presented in a concise, but comprehensible way, such that further ramifications and future directions can be immediately seen.

Advances in Harmonic Analysis and Partial Differential Equations
Michael Ruzhansky, Vladimir Georgiev, Tohru Ozawa, Jens Wirth
 Birkhäuser
 7 Novembre 2020
 9783030582159
This book originates from the session "Harmonic Analysis and Partial Differential Equations" held at the 12th ISAAC Congress in Aveiro, and provides a quick overview over recent advances in partial differential equations with a particular focus on the interplay between tools from harmonic analysis, functional inequalities and variational characterisations of solutions to particular nonlinear PDEs. It can serve as a useful source of information to mathematicians, scientists and engineers.
The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a stateoftheart overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area. 
Harmonic Analysis and Partial Differential Equations
Michael Ruzhansky, Jens Wirth
 Birkhäuser
 6 Mars 2023
 9783031243110
This book collects papers related to the session "Harmonic Analysis and Partial Differential Equations" held at the 13th International ISAAC Congress in Ghent and provides an overview on recent trends and advances in the interplay between harmonic analysis and partial differential equations. The book can serve as useful source of information for mathematicians, scientists and engineers.
The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a stateoftheart overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area. 
Extended Abstracts 2021/2022
Michael Ruzhansky, Duvan Cardona, Joel Restrepo
 Birkhäuser
 28 Février 2024
 9783031485794
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. The volume has two main topics:
1. Analysis and PDEs. The volume presents recent results in fundamental problems for solving partial integrodifferential equations in different settings such as Euclidean spaces, manifolds, Banach spaces, and many others. Discussions about the global and local solvability using microlocal and harmonic analysis methods, studies of new techniques and approaches arising from a physical perspective or the mathematical point of view have also been included. Several connected branches arising in this regard are shown.
2. Geometric analysis. The volume presents studies of modern techniques for elliptic and subelliptic PDEs that in recent times have been used to establish new results in differential geometry and differential topology. These topics involve the intrinsic research in microlocal analysis, geometric analysis, and harmonic analysis abroad. Different problems having relevant geometric information for different applications in mathematical physics and other problems of classification have been considered. 
Extended Abstracts MWCAPDE 2023
Michael Ruzhansky, Berikbol Torebek
 Birkhäuser
 1 Avril 2024
 9783031416651
This collection consists of selected scientific results stemming from the conference "Methusalem Workshop on Classical Analysis and PDEs", held at the Ghent University from 27th February 2023 to 1st March 2023. The workshop was organized by the "Ghent Analysis & PDE Center". The presented materials mainly consist of scientific results on classical analysis and problems of PDEs. In particular, results on harmonic analysis, functional spaces, functional inequalities, inverse problems, nonlocal PDEs, nonclassical problems of PDEs, integrodifferential equations, hypoelliptic operators, pseudodifferential calculus, and others are given.

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Analysis of Infectious Disease Problems (Covid19) and Their Global Impact
Michael Ruzhansky, Praveen Agarwal, Delfim F. M. Torres, Juan J. Nieto
 Springer
 29 Septembre 2021
 9789811624506
This edited volume is a collection of selected research articles discussing the analysis of infectious diseases by using mathematical modelling in recent times. Divided into two parts, the book gives a general and countrywise analysis of Covid19. Analytical and numerical techniques for virus models are presented along with the application of mathematical modelling in the analysis of their spreading rates and treatments. The book also includes applications of fractional differential equations as well as ordinary, partial and integrodifferential equations with optimization methods. Probability distribution and their biomathematical applications have also been studied. This book is a valuable resource for researchers, scholars, biomathematicians and medical experts.