Product Description
Moment Theory is not a new subject; however, in classical treatments, the ill-posedness of the problem is not taken into account - hence this monograph. Assuming a "true" solution to be uniquely determined by a sequence of moments (given as integrals) of which only finitely many are inaccurately given, the authors describe and analyze several regularization methods and derive stability estimates. Mathematically, the task often consists in the reconstruction of an analytic or harmonic function, as is natural from concrete applications discussed (e.g. inverse heat conduction problems, Cauchy's problem for the Laplace equation, gravimetry). The book can be used in a graduate or upper undergraduate course in Inverse Problems, or as supplementary reading for a course on Applied Partial Differential Equations. ... Read more

Product Description

This book develops the potential theory starting from a sub-Markovian resolvent of kernels on a measurable space, covering the context offered by a right process with general state space. It turns out that the main results from the classical cases (e.g., on locally compact spaces, with Green functions) have meaningful extensions to this setting. The study of the strongly supermedian functions and specific methods like the Revuz correspondence, for the largest class of measures, and the weak duality between two sub-Markovian resolvents of kernels are presented for the first time in a complete form. It is shown that the quasi-regular semi-Dirichlet forms fit in the weak duality hypothesis. Further results are related to the subordination operators and measure perturbations. The subject matter is supplied with a probabilistic counterpart, involving the homogeneous random measures, multiplicative, left and co-natural additive functionals.

The book is almost self-contained, being accessible to graduate students.

Product Description
The purpose of this book is to give a streamlinedintroduction to the theoryof (not necessarily symmetric)Dirichlet forms on general state spaces. Itincludes boththe analytic and probabilistic components of the theory.Asubstantial part of the book is designed for a one-yeargraduate course: it provides a framework which covers boththe well-studied "classical" theoryof regular Dirichletforms on locally compact state spaces and allrecentextensions to infinite-dimensional state spaces. Among otherthings it contains a complete proof of an analyticcharacterization of the class of Dirichlet forms which areassociated with right continuous strong Markov processes,i.e., those having a probabilistic counterpart. This solvesa long-standing openproblem of the theory.Finally, a general regularization method is developedwhichmakes it possible to transfer all results known in theclassicallocally compact regular case to this (in the abovesense) most general classof Dirichlet forms. ... Read more

Product Description
"..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society ... Read more

Product Description
The purpose of this book is to develop the foundations of potential theory and rational dynamics on the Berkovich projective line over an arbitrary complete, algebraically closed non-Archimedean field. In addition to providing a concrete and ``elementary'' introduction to Berkovich analytic spaces and to potential theory and rational iteration on the Berkovich line, the book contains applications to arithmetic geometry and arithmetic dynamics. A number of results in the book are new, and most have not previously appeared in book form. Three appendices--on analysis, $\mathbb{R}$-trees, and Berkovich's general theory of analytic spaces--are included to make the book as self-contained as possible. The authors first give a detailed description of the topological structure of the Berkovich projective line and then introduce the Hsia kernel, the fundamental kernel for potential theory. Using the theory of metrized graphs, they define a Laplacian operator on the Berkovich line and construct theories of capacities, harmonic and subharmonic functions, and Green's functions, all of which are strikingly similar to their classical complex counterparts. After developing a theory of multiplicities for rational functions, they give applications to non-Archimedean dynamics, including local and global equidistribution theorems, fixed point theorems, and Berkovich space analogues of many fundamental results from the classical Fatou-Julia theory of rational iteration. They illustrate the theory with concrete examples and exposit Rivera-Letelier's results concerning rational dynamics over the field of $p$-adic complex numbers. They also establish Berkovich space versions of arithmetic results such as the Fekete-Szego theorem and Bilu's equidistribution theorem. ... Read more

Product Description
The Cauchy integral formula is the most central result in all of classical function theory. A recent discovery of Kerzman and Stein allows more theorems than ever to be deduced from simple facts about the Cauchy integral.In this book, the Riemann Mapping Theorem is deduced, the Dirichlet and Neumann problems for the Laplace operator are solved, the Poisson kernal is constructed, and the inhomogenous Cauchy-Reimann equations are solved concretely using formulas stemming from the Kerzman-Stein result. These explicit formulas yield new numerical methods for computing the classical objects of potential theory and conformal mapping, and the book provides succinct, complete explanations of these methods.The Cauchy Transform, Potential Theory, and Conformal Mapping is suitable for pure and applied math students taking a beginning graduate-level topics course on aspects of complex analysis. It will also be useful to physicists and engineers interested in a clear exposition on a fundamental topic of complex analysis, methods, and their application. ... Read more

Product Description
This book constitutes an anthology of refereed papers arranged to acknowledge the work of Wilfried Brauer on the occasion of his sixtieth birthday. The volume presents 49 revised refereed papers organized in topical sections on computer science and its potential, social implications of computer science, formal languages and automata, structures and complexity theory, Petri nets, systems analysis and distributed systems, software engineering and verification, cognition and artificial intelligence, knowledge representation and reasoning, machine learning, neural networks and robotics, language and information systems. ... Read more