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  • Classical Fine Potential Theory

    Series series Mathematics and Statistics (R0)
    This comprehensive book explores the intricate realm of fine potential theory. Delving into the real theory, it navigates through harmonic and subharmonic functions, addressing the famed Dirichlet problem within finely open sets of R^n. These sets are defined relative to the coarsest topology on R^n, ensuring the continuity of all subharmonic functions. This theory underwent extensive scrutiny ... Leer más

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  • Handbook of Measure Theory

    In two volumes

    de E. Pap ...
    The main goal of this Handbook isto survey measure theory with its many different branches and itsrelations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications whichsupport the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are ... Leer más

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  • Brownian Motion, Martingales, and Stochastic Calculus

    Series series Mathematics and Statistics (R0)
    This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov ... Leer más

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  • Linear Groups

    The Accent on Infinite Dimensionality

    Series series Chapman & Hall/CRC Monographs and Research Notes in Mathematics
    Linear Groups: The Accent on Infinite Dimensionality explores some of the main results and ideas in the study of infinite-dimensional linear groups. The theory of finite dimensional linear groups is one of the best developed algebraic theories. The array of articles devoted to this topic is enormous, and there are many monographs concerned with matrix groups, ranging from old, classical texts to ... Leer más

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  • Topological Methods in the Study of Boundary Value Problems

    de Pablo Amster ...
    Series series Mathematics and Statistics (R0)
    This textbook is devoted to the study of some simple but representative nonlinear boundary value problems by topological methods. The approach is elementary, with only a few model ordinary differential equations and applications, chosen in such a way that the student may avoid most of the technical difficulties and focus on the application of topological methods. Only basic knowledge of general ... Leer más

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  • Harmonic And Spectral Analysis

    This book provides a modern introduction to harmonic analysis and synthesis on topological groups. It serves as a guide to the abstract theory of Fourier transformation. For the first time, it presents a detailed account of the theory of classical harmonic analysis together with the recent developments in spectral analysis and synthesis. ... Leer más

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  • The Finite Element Method for Elliptic Problems

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    Series Libro 4 - Studies in Mathematics and its Applications
    The objective of this book is to analyze within reasonable limits (it is not a treatise) the basic mathematical aspects of the finite element method. The book should also serve as an introduction to current research on this subject. On the one hand, it is also intended to be a working textbook for advanced courses in Numerical Analysis, as typically taught in graduate courses in American and ... Leer más

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  • Analysis

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    Series series Mathematics and Statistics (R0)
    This textbook covers the main results and methods of real analysis in a single volume. Taking a progressive approach to equations and transformations, this book starts with the very foundations of real analysis (set theory, order, convergence, and measure theory) before presenting powerful results that can be applied to concrete problems.In addition to classical results of functional analysis, ... Leer más

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  • I: Functional Analysis

    Series Libro 1 - Methods of Modern Mathematical Physics
    This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later ... Leer más

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  • Optimization and Differentiation

    Series series Chapman & Hall/CRC Monographs and Research Notes in Mathematics
    Optimization and Differentiation is an introduction to the application of optimization control theory to systems described by nonlinear partial differential equations. As well as offering a useful reference work for researchers in these fields, it is also suitable for graduate students of optimal control theory. ... Leer más

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  • Stochastic Partial Differential Equations

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    Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary ... Leer más

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  • Nonlinear Elliptic Partial Differential Equations

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    This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations.After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite ... Leer más

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