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  • Fractals in Probability and Analysis

    Series Book 162 - Cambridge Studies in Advanced Mathematics
    This is a mathematically rigorous introduction to fractals which emphasizes examples and fundamental ideas. Building up from basic techniques of geometric measure theory and probability, central topics such as Hausdorff dimension, self-similar sets and Brownian motion are introduced, as are more specialized topics, including Kakeya sets, capacity, percolation on trees and the traveling salesman ... Read more

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    Now that people are aware that data can make the difference in an election or a business model, data science as an occupation is gaining ground. But how can you get started working in a wide-ranging, interdisciplinary field that’s so clouded in hype? This insightful book, based on Columbia University’s Introduction to Data Science class, tells you what you need to know.In many of these chapter ... Read more

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  • Pseudodifferential Equations Over Non-Archimedean Spaces

    Series series Mathematics and Statistics (R0)
    Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular ... Read more

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  • Probability on Compact Lie Groups

    Series Book 70 - Probability Theory and Stochastic Modelling
    Probability theory on compact Lie groups deals with the interaction between “chance” and “symmetry,” a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an ... Read more

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  • Extensions of Positive Definite Functions

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    Series series Mathematics and Statistics (R0)
    This monograph deals with the mathematics of extending given partial data-sets obtained from experiments;Experimentalists frequently gather spectral data when the observed data is limited, e.g., by the precision of instruments; or by other limiting external factors. Here the limited information is a restriction, and the extensions take the form of full positive definite function on some prescribed ... Read more

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  • Concentration Inequalities for Sums and Martingales

    Series series Mathematics and Statistics (R0)
    The purpose of this book is to provide an overview of historical and recent results on concentration inequalities for sums of independent random variables and for martingales.The first chapter is devoted to classical asymptotic results in probability such as the strong law of large numbers and the central limit theorem. Our goal is to show that it is really interesting to make use of concentration ... 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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  • A First Course in Analysis

    Series series Cambridge Mathematical Textbooks
    This rigorous textbook is intended for a year-long analysis or advanced calculus course for advanced undergraduate or beginning graduate students. Starting with detailed, slow-paced proofs that allow students to acquire facility in reading and writing proofs, it clearly and concisely explains the basics of differentiation and integration of functions of one and several variables, and covers the ... Read more

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  • Inequalities In Analysis And Probability (Second Edition)

    by Odile Pons ...
    The book is aimed at graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and functional spaces with applications to probability. It also develops new extensions of the analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales and to ... Read more

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  • Pluripotential Theory

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    Pluripotential theory is a very powerful tool in geometry, complex analysis and dynamics. This volume brings together the lectures held at the 2011 CIME session on "pluripotential theory" in Cetraro, Italy. This CIME course focused on complex Monge-Ampére equations, applications of pluripotential theory to Kahler geometry and algebraic geometry and to holomorphic dynamics. The contributions ... Read more

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  • Harmonic and Subharmonic Function Theory on the Hyperbolic Ball

    by Manfred Stoll ...
    Series Book 431 - London Mathematical Society Lecture Note Series
    This comprehensive monograph is ideal for established researchers in the field and also graduate students who wish to learn more about the subject. The text is made accessible to a broad audience as it does not require any knowledge of Lie groups and only a limited knowledge of differential geometry. The author's primary emphasis is on potential theory on the hyperbolic ball, but many other ... 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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