Joachim Toft - Böcker

This book includes the texts of the survey lectures given by plenary speakers at the 11th International ISAAC Congress held in Växjö, Sweden, on 14-18 August, 2017. It is the purpose of ISAAC to promote analysis, its applications, and its interaction with computation. Analysis is understood here in the broad sense of the word, including differential equations, integral equations, functional analysis, and function theory. With this objective, ISAAC organizes international Congresses for the presentation and discussion of research on analysis.The plenary lectures in the present volume, authored by eminent specialists, are devoted to some exciting recent developments, topics including: local solvability for subprincipal type operators; fractional-order Laplacians; degenerate complex vector fields in the plane; lower bounds for pseudo-differential operators; a survey on Morrey spaces; localization operators in Signal Theory and Quantum Mechanics.  Thanks to theaccessible style used, readers only need a basic command of Calculus.This book will appeal to scientists, teachers, and graduate students in Mathematics, in particular Mathematical Analysis, Probability and Statistics, Numerical Analysis and Mathematical Physics.

This book is a collection of short papers from the 11th International ISAAC Congress 2017 in Växjö, Sweden. The papers, written by the best international experts, are devoted to recent results in mathematics with a focus on analysis.

Thanks to theaccessible style used, readers only need a basic command of Calculus.This book will appeal to scientists, teachers, and graduate students in Mathematics, in particular Mathematical Analysis, Probability and Statistics, Numerical Analysis and Mathematical Physics.

This volume contains the contributions of the participants of the 12th ISAAC congress which was held at the University of Aveiro, Portugal, from July 29 to August 3, 2019. These contributions originate from the following sessions: Applications of dynamical systems theory in biology, Complex Analysis and Partial Differential Equations, Complex Geometry, Complex Variables and Potential Theory, Constructive Methods in the Theory of Composite and Porous Media, Function Spaces and Applications, Generalized Functions and Applications, Geometric & Regularity Properties of Solutions to Elliptic and Parabolic PDEs, Geometries Defined by Differential Forms, Partial Differential Equations on Curved Spacetimes, Partial Differential Equations with Nonstandard Growth, Quaternionic and Clifford Analysis, Recent Progress in Evolution Equations, Wavelet theory and its Related Topics.

This volume contains the contributions of the participants of the 14th ISAAC congress, held at the University of São Paulo, Campus Ribeirão Preto, Brazil, on July 17-21, 2023.

This volume consists of twenty peer-reviewed papers from the special session on pseudodifferential operators and the special session on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples’ Friendship University of Russia in Moscow on August 22‒27, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifolds with edges, heat kernels and Green functions of sub-Laplacians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, Lp-boundedness of pseudo-differential operators on the torus, and pseudo-differential operators related to time-frequency analysis. The second group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlinear differential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differential equations. This second group of papers are related to the third collection of papers via the setting of Colombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volume contains the synergies of the three areas treated and is a useful complement to volumes 155, 164, 172, 189, 205 and 213 published in the same series in, respectively, 2004, 2006, 2007, 2009, 2010 and 2011.

This volume consists of twenty peer-reviewed papers from the special session on pseudodifferential operators and the special session on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples’ Friendship University of Russia in Moscow on August 22‒27, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifolds with edges, heat kernels and Green functions of sub-Laplacians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, Lp-boundedness of pseudo-differential operators on the torus, and pseudo-differential operators related to time-frequency analysis. The second group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlinear differential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differential equations. This second group of papers are related to the third collection of papers via the setting of Colombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volume contains the synergies of the three areas treated and is a useful complement to volumes 155, 164, 172, 189, 205 and 213 published in the same series in, respectively, 2004, 2006, 2007, 2009, 2010 and 2011.

Topics include Columbeau algebras, ultra-distributions, partial differential equations, micro-local analysis, harmonic analysis, global analysis, geometry, quantization, mathematical physics, and time-frequency analysis.

Topics include Columbeau algebras, ultra-distributions, partial differential equations, micro-local analysis, harmonic analysis, global analysis, geometry, quantization, mathematical physics, and time-frequency analysis.

This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis.

This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis.

Pseudo-differential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century.The volume investigates the mathematics of quantization and signals in the context of pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted.

As a satellite conference to the Fourth Congress of European Mathematics held at StockholmUniversityin2004,theInternationalConferenceonPseudo-Di?erential Operators and Related Topics was held at V.. axjo .. University in Sweden from June 22 to June 25, 2004. The conferencewas supported by Vaxj .. oU .. niversity,theFIRB Research Group on Microlocal Analysis of Universit' a di Torino, and the Int- national Society for Analysis, its Applications and Computation (ISAAC). The conferencewas well attended by about 50 mathematicians fromBulgaria,Canada, Denmark, England,Finland, Germany,Italy, Japan,Mexico, Serbiaand Monte- gro, Russia and Sweden. The conference covered a broad spectrum of topics related to pseudo-di?erential operators such as partial di?erential equations, quantization, Wigner transforms andWeyltransformsonLiegroups,mathematicalphysics,time-frequencyanalysis and stochastic processes. The speakers were enthusiastic about the prospect of publishing articles based on their presentations in a volume to be published in Professor Israel Gohberg's prestigious series entitled "Operator Theory: Advances and Applications".All contributions from speakers have been carefully refereed and the articles c- lected in this volume give a representative ?avour of the mathematics presented at the conference. This volume is a permanent record of the conference and a valuable complement to the volume "Advances in Pseudo-Di?erential Operators" published in the same series in 2004, which is devoted to the Special Session on Pseudo-Di?erential Operators at the Fourth ISAAC Congress held at York U- versity in August 2003. Operator Theory: Advances and Applications, Vol. 164, 1-21 c 2006 Birkh. auser Verlag Basel/Switzerland Strongly Elliptic Second Order Systems with Spectral Parameter in Transmission Conditions on a Nonclosed Surface M. S.