Dirichlet Forms and Related Topics
Title | Dirichlet Forms and Related Topics PDF eBook |
Author | Zhen-Qing Chen |
Publisher | Springer Nature |
Pages | 572 |
Release | 2022-09-04 |
Genre | Mathematics |
ISBN | 9811946728 |
This conference proceeding contains 27 peer-reviewed invited papers from leading experts as well as young researchers all over the world in the related fields that Professor Fukushima has made important contributions to. These 27 papers cover a wide range of topics in probability theory, ranging from Dirichlet form theory, Markov processes, heat kernel estimates, entropy on Wiener spaces, analysis on fractal spaces, random spanning tree and Poissonian loop ensemble, random Riemannian geometry, SLE, space-time partial differential equations of higher order, infinite particle systems, Dyson model, functional inequalities, branching process, to machine learning and Hermitizable problems for complex matrices. Researchers and graduate students interested in these areas will find this book appealing.
Analysis and Geometry of Metric Measure Spaces
Title | Analysis and Geometry of Metric Measure Spaces PDF eBook |
Author | Galia Devora Dafni |
Publisher | American Mathematical Soc. |
Pages | 241 |
Release | 2013 |
Genre | Mathematics |
ISBN | 0821894188 |
Contains lecture notes from most of the courses presented at the 50th anniversary edition of the Seminaire de Mathematiques Superieure in Montreal. This 2011 summer school was devoted to the analysis and geometry of metric measure spaces, and featured much interplay between this subject and the emergent topic of optimal transportation.
From Classical Analysis to Analysis on Fractals
Title | From Classical Analysis to Analysis on Fractals PDF eBook |
Author | Patricia Alonso Ruiz |
Publisher | Springer Nature |
Pages | 294 |
Release | 2023-11-25 |
Genre | Mathematics |
ISBN | 3031378008 |
Over the course of his distinguished career, Robert Strichartz (1943-2021) had a substantial impact on the field of analysis with his deep, original results in classical harmonic, functional, and spectral analysis, and in the newly developed analysis on fractals. This is the first volume of a tribute to his work and legacy, featuring chapters that reflect his mathematical interests, written by his colleagues and friends. An introductory chapter summarizes his broad and varied mathematical work and highlights his profound contributions as a mathematical mentor. The remaining articles are grouped into three sections – functional and harmonic analysis on Euclidean spaces, analysis on manifolds, and analysis on fractals – and explore Strichartz’ contributions to these areas, as well as some of the latest developments.
Geometric Control Theory and Sub-Riemannian Geometry
Title | Geometric Control Theory and Sub-Riemannian Geometry PDF eBook |
Author | Gianna Stefani |
Publisher | Springer |
Pages | 385 |
Release | 2014-06-05 |
Genre | Mathematics |
ISBN | 331902132X |
Honoring Andrei Agrachev's 60th birthday, this volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume, etc.
Fokker-Planck-Kolmogorov Equations
Title | Fokker-Planck-Kolmogorov Equations PDF eBook |
Author | Vladimir I. Bogachev |
Publisher | American Mathematical Soc. |
Pages | 495 |
Release | 2015-12-17 |
Genre | Mathematics |
ISBN | 1470425580 |
This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.
Diffraction of Singularities for the Wave Equation on Manifolds with Corners
Title | Diffraction of Singularities for the Wave Equation on Manifolds with Corners PDF eBook |
Author | Richard B. Melrose |
Publisher | |
Pages | 148 |
Release | 2013 |
Genre | Mathematics |
ISBN |
The authors consider the fundamental solution to the wave equation on a manifold with corners of arbitrary codimension. If the initial pole of the solution is appropriately situated, the authors show that the singularities which are diffracted by the corners (i.e., loosely speaking, are not propagated along limits of transversely reflected rays) are smoother than the main singularities of the solution. More generally, the authors show that subject to a hypothesis of nonfocusing, diffracted wavefronts of any solution to the wave equation are smoother than the incident singularities. These results extend the authors' previous work on edge manifolds to a situation where the fibers of the boundary fibration, obtained here by blowup of the corner in question, are themselves manifolds with corners.
Revista Matemática Iberoamericana
Title | Revista Matemática Iberoamericana PDF eBook |
Author | |
Publisher | |
Pages | 782 |
Release | 2015 |
Genre | Mathematics |
ISBN |