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  • An Introduction to the Theory of Reproducing Kernel Hilbert Spaces

    Series Book 152 - Cambridge Studies in Advanced Mathematics
    Reproducing kernel Hilbert spaces have developed into an important tool in many areas, especially statistics and machine learning, and they play a valuable role in complex analysis, probability, group representation theory, and the theory of integral operators. This unique text offers a unified overview of the topic, providing detailed examples of applications, as well as covering the fundamental ... Read more

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    by Steven Taylor ...
    Markov ModelsThis book will offer you an insight into the Hidden Markov Models as well as the Bayesian Networks. Additionally, by reading this book, you will also learn algorithms such as Markov Chain Sampling.Furthermore, this book will also teach you how Markov Models are very relevant when a decision problem is associated with a risk that continues over time, when the timing of occurrenc... ... Read more

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  • Martingales in Banach Spaces

    by Gilles Pisier ...
    Series Book 155 - Cambridge Studies in Advanced Mathematics
    This book focuses on the major applications of martingales to the geometry of Banach spaces, and a substantial discussion of harmonic analysis in Banach space valued Hardy spaces is also presented. It covers exciting links between super-reflexivity and some metric spaces related to computer science, as well as an outline of the recently developed theory of non-commutative martingales, which has ... Read more

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  • Computer Algebra in Quantum Field Theory

    Integration, Summation and Special Functions

    Series series Computer Science (R0)
    The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from ... Read more

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  • Multi-Layer Potentials and Boundary Problems

    for Higher-Order Elliptic Systems in Lipschitz Domains

    Series series Mathematics and Statistics (R0)
    Many phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator in a given domain. When the differential operator under discussion is of second order a variety of tools are available for dealing with such problems, including boundary integral methods, variational methods, harmonic measure techniques, and methods ... Read more

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  • Hyponormal Quantization of Planar Domains

    Exponential Transform in Dimension Two

    Series series Mathematics and Statistics (R0)
    This book exploits the classification of a class of linear bounded operators with rank-one self-commutators in terms of their spectral parameter, known as the principal function. The resulting dictionary between two dimensional planar shapes with a degree of shade and Hilbert space operators turns out to be illuminating and beneficial for both sides. An exponential transform, essentially a Riesz ... Read more

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  • Beyond Wavelets

    Edited by Grant Welland ...
    Series Book 10 - Studies in Computational Mathematics
    "Beyond Wavelets" presents state-of-the-art theories, methods, algorithms, and applications of mathematical extensions for classical wavelet analysis. Wavelets, introduced 20 years ago byMorlet and Grossmann and developed very rapidly during the 1980's and 1990's, has created a common link between computational mathematics and other disciplines of science and engineering.Classical wavelets have ... Read more

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  • A Primer on the Dirichlet Space

    Series Book 203 - Cambridge Tracts in Mathematics
    The Dirichlet space is one of the three fundamental Hilbert spaces of holomorphic functions on the unit disk. It boasts a rich and beautiful theory, yet at the same time remains a source of challenging open problems and a subject of active mathematical research. This book is the first systematic account of the Dirichlet space, assembling results previously only found in scattered research articles ... Read more

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  • Geometric Methods in PDE’s

    Series series Springer Nature Proceedings excluding Computer Science
    The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts ... Read more

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  • Distributions, Partial Differential Equations, and Harmonic Analysis

    by Dorina Mitrea ...
    Series series Mathematics and Statistics (R0)
    The theory of distributions constitutes an essential tool in the study of partial differential equations. This textbook would offer, in a concise, largely self-contained form, a rapid introduction to the theory of distributions and its applications to partial differential equations, including computing fundamental solutions for the most basic differential operators: the Laplace, heat, wave, Lam\'e ... Read more

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  • Invariant Probabilities of Transition Functions

    Series series Mathematics and Statistics (R0)
    The structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other ... Read more

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  • Functional Analysis

    Fundamentals and Applications

    by Michel Willem ...
    Series series Mathematics and Statistics (R0)
    The goal of this work is to present the principles of functional analysis in a clear and concise way. The first three chapters of Functional Analysis: Fundamentals and Applications describe the general notions of distance, integral and norm, as well as their relations. The three chapters that follow deal with fundamental examples: Lebesgue spaces, dual spaces and Sobolev spaces. Two subsequent ... Read more

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