The topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on spaces of homogeneous type, topology, and quasi-metric geometry.
This text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications.
This textbook describes selected topics in functional analysis as powerful tools of immediate use in many fields within applied mathematics, physics and engineering.
This monograph provides the theoretical foundations needed for the construction of fundamental solutions and fundamental matrices of (systems of) linear partial differential equations.
This volume presents a unified approach to constructing iterative methods for solving irregular operator equations and provides rigorous theoretical analysis for several classes of these methods.
This self-contained book lays the foundations for a systematic understanding of potential theoretic and uniformization problems on fractal Sierpinski carpets, and proposes a theory based on the latest developments in the field of analysis on metric spaces.
This book explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research.
Limit theorems for random sequences may conventionally be divided into two large parts, one of them dealing with convergence of distributions (weak limit theorems) and the other, with almost sure convergence, that is to say, with asymptotic prop- erties of almost all sample paths of the sequences involved (strong limit theorems).
This book contains plenary lectures given at the International Conference on Mathematical and Computational Modeling, Approximation and Simulation, dealing with three very different problems: reduction of Runge and Gibbs phenomena, difficulties arising when studying models that depend on the highly nonlinear behaviour of a system of PDEs, and data fitting with truncated hierarchical B-splines for the adaptive reconstruction of industrial models.
In its second installment, Innovative Integrals and Their Applications II explores multidimensional integral identities, unveiling powerful techniques for attacking otherwise intractable integrals, thus demanding ingenuity and novel approaches.
Designed for senior undergraduate and graduate students in mathematics, this textbook offers a comprehensive exploration of measure theory and integration.
Measure, Integral and Probability is a gentle introduction that makes measure and integration theory accessible to the average third-year undergraduate student.
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.
Since long over the decades there has been a large transversal community of mathematicians grappling with the sophisticated challenges of the rigorous modelling and the spectral and scattering analysis of quantum systems of particles subject to an interaction so much localised to be considered with zero range.
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.
This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering.
Many problems in mathematical physics rely heavily on the use of elliptical partial differential equations, and boundary integral methods play a significant role in solving these equations.
