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Structured population models are transport-type equations often applied to describe evolution of heterogeneous populations of biological cells, animals or humans, including phenomena such as crowd dynamics or pedestrian flows. This book introduces the mathematical underpinnings of these applications, providing a comprehensive analytical framework for structured population models in spaces of Radon measures. The unified approach allows for the study of transport processes on structures that are not vector spaces (such as traffic flow on graphs) and enables the analysis of the numerical algorithms used in applications. Presenting a coherent account of over a decade of research in the area, the text includes appendices outlining the necessary background material and discusses current trends in the theory, enabling graduate students to jump quickly into research.

Population --- Functions of bounded variation. --- Lipschitz spaces. --- Metric spaces. --- Radon measures. --- Biology --- Mathematical models. --- Biological models --- Biomathematics --- Measures, Radon --- Measure theory --- Vector-valued measures --- Spaces, Metric --- Generalized spaces --- Set theory --- Topology --- Hölder spaces --- Function spaces --- Bounded variables, Functions of --- Bounded variation, Functions of --- BV functions --- Functions of bounded variables --- Functions of real variables

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Embeddings of discrete metric spaces into Banach spaces recently became an important tool in computer science and topology. The purpose of the book is to present some of the most important techniques and results, mostly on bilipschitz and coarse embeddings. The topics include: (1) Embeddability of locally finite metric spaces into Banach spaces is finitely determined; (2) Constructions of embeddings; (3) Distortion in terms of Poincaré inequalities; (4) Constructions of families of expanders and of families of graphs with unbounded girth and lower bounds on average degrees; (5) Banach spaces which do not admit coarse embeddings of expanders; (6) Structure of metric spaces which are not coarsely embeddable into a Hilbert space; (7) Applications of Markov chains to embeddability problems; (8) Metric characterizations of properties of Banach spaces; (9) Lipschitz free spaces. Substantial part of the book is devoted to a detailed presentation of relevant results of Banach space theory and graph theory. The final chapter contains a list of open problems. Extensive bibliography is also included. Each chapter, except the open problems chapter, contains exercises and a notes and remarks section containing references, discussion of related results, and suggestions for further reading. The book will help readers to enter and to work in a very rapidly developing area having many important connections with different parts of mathematics and computer science.

Banach spaces. --- Lipschitz spaces. --- Stochastic partial differential equations. --- Banach spaces, Stochastic differential equations in --- Hilbert spaces, Stochastic differential equations in --- SPDE (Differential equations) --- Stochastic differential equations in Banach spaces --- Stochastic differential equations in Hilbert spaces --- Differential equations, Partial --- Hölder spaces --- Function spaces --- Functions of complex variables --- Generalized spaces --- Topology --- Banach Space Theory. --- Bilipschitz Embedding. --- Coarse Embedding. --- Embedding of Discrete Metric Spaces. --- Functional Analysis. --- Graph Theory.

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A collection of invited chapters dedicated to Carlos Segovia, this unified and self-contained volume examines recent developments in real and harmonic analysis. The work begins with a chronological description of Segovia’s mathematical life, his original ideas and their evolution, which may be a source of inspiration for many mathematicians working in the fields of harmonic analysis, functional analysis, and partial differential equations. Apart from this contribution, two different types of chapters are featured in the work: surveys dealing with Carlos’ favorite topics, and PDE works written by students and colleagues close to Segovia whose careers were in some way influenced by him. Specific topics covered include: * Vector-valued singular integral equations * Harmonic analysis related to Hermite expansions * Gas flow in porous media * Global well-posedness of the KPI Equation * Monge–Ampère type equations and applications * Spaces of homogeneous type * Hardy and Lipschitz spaces * One-sided operators This book will be useful to graduate students as well as pure and applied mathematicians interested in new mathematical developments in areas related to real and harmonic analysis. Contributors: H. Aimar, A. Bonami, O. Blasco, L.A. Caffarelli, S. Chanillo, J. Feuto, L. Forzani, C.E. Gutíerrez, E. Harboure, A.L. Karakhanyan, C.E. Kenig, R.A. Macías, J.J. Manfredi, F.J. Martín-Reyes, P. Ortega, R. Scotto, A. de la Torre, J.L. Torrea.

Hardy spaces. --- Harmonic analysis. --- Harmonic functions. --- Lipschitz spaces. --- Harmonic analysis --- Harmonic functions --- Hardy spaces --- Lipschitz spaces --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Hölder spaces --- Functions, Harmonic --- Laplace's equations --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Spaces, Hardy --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Fourier analysis. --- Partial differential equations. --- Functions of real variables. --- Applied mathematics. --- Engineering mathematics. --- Abstract Harmonic Analysis. --- Fourier Analysis. --- Real Functions. --- Analysis. --- Partial Differential Equations. --- Appl.Mathematics/Computational Methods of Engineering. --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Time-series analysis --- Function spaces --- Differential equations, Partial --- Lamé's functions --- Spherical harmonics --- Toroidal harmonics --- Functional analysis --- Functions of complex variables --- Global analysis (Mathematics). --- Differential equations, partial. --- Mathematical and Computational Engineering. --- Analysis, Global (Mathematics) --- Differential topology --- Geometry, Algebraic --- Math --- Science --- Analysis, Fourier --- Engineering --- Engineering analysis --- Partial differential equations --- 517.1 Mathematical analysis --- Real variables