Spectral Analysis on Graph-Like Spaces

Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analy

Analysis of functions on the finite dimensional Euclidean space with respect to the Lebesgue measure is fundamental in mathematics. The extension to infinite dimension is a great challenge due to the

This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introduct

Several natural Lp spaces of analytic functions have been widely studied in the past few decades, including Hardy spaces, Bergman spaces, and Fock spaces. The terms “Hardy spaces” and “Bergman spaces”

Analysis on Function Spaces of Musielak-Orlicz Type provides a state-of-the-art survey on the theory of function spaces of Musielak-Orlicz type. The book also offers readers a step-by-step introductio

This book is suitable for advanced undergraduate and graduate students in mathematics with a strong background in linear algebra and advanced calculus. Early chapters develop representation theory of

This book addresses the analysis of musical sounds from the viewpoint of someone at the intersection between physicists, engineers, piano technicians, and musicians.The study is structured into three

These notes originated from a course given by the first author in 1998/99 in the Scuola Normale Superiore of Pisa. The aim of the course was the presentation of the main mathematical prerequisites nee

The dramatic changes that came about in analysis during the twentieth century are truly amazing. In the thirties, complex methods and Fourier series played a seminal role. After many improvements, mos

This book contains the notes of an international summer school on Analysis in Metric Spaces. The contributions are the following: T. Coulhon, Random walks and geometry on infinite graphs; G. David, Un

Foliated spaces look locally like products, but their global structure is generally not a product, and tangential differential operators are correspondingly more complex. In the 1980s, Alain Connes founded what is now known as noncommutative geometry and topology. One of the first results was his generalization of the Atiyah-Singer index theorem to compute the analytic index associated with a tangential (pseudo) - differential operator and an invariant transverse measure on a foliated manifold, in terms of topological data on the manifold and the operator. This second edition presents a complete proof of this beautiful result, generalized to foliated spaces (not just manifolds). It includes the necessary background from analysis, geometry, and topology. The present edition has improved exposition, an updated bibliography, an index, and additional material covering developments and applications since the first edition came out, including the confirmation of the Gap Labeling Conjecture

Ambrosio and Tilli's (mathematics, Scuola Normale Superiore, Pisa) textbook is based on a course given by Ambrosio at the Scuola in 1998-1999, presenting the main mathematical prerequisites needed for

The purpose of this book is to communicate some of the recent advances in this field while preparing the reader for more advanced study. The material can be roughly divided into three different types:

This book provides a comprehensive introduction to Fock space theory and its applications to mathematical quantum field theory. The first half of the book, Part I, is devoted to detailed descriptions

A large part of mathematical analysis, both pure and applied, takes place on Polish spaces: topological spaces whose topology can be given by a complete metric. This analysis is not only simpler than in the general case, but, more crucially, contains many important special results. This book provides a detailed account of analysis and measure theory on Polish spaces, including results about spaces of probability measures. Containing more than 200 elementary exercises, it will be a useful resource for advanced mathematical students and also for researchers in mathematical analysis. The book also includes a straightforward and gentle introduction to the theory of optimal transportation, illustrating just how many of the results established earlier in the book play an essential role in the theory.

A large part of mathematical analysis, both pure and applied, takes place on Polish spaces: topological spaces whose topology can be given by a complete metric. This analysis is not only simpler than in the general case, but, more crucially, contains many important special results. This book provides a detailed account of analysis and measure theory on Polish spaces, including results about spaces of probability measures. Containing more than 200 elementary exercises, it will be a useful resource for advanced mathematical students and also for researchers in mathematical analysis. The book also includes a straightforward and gentle introduction to the theory of optimal transportation, illustrating just how many of the results established earlier in the book play an essential role in the theory.

This text is an introduction to harmonic analysis on symmetric spaces, focusing on advanced topics such as higher rank spaces, positive definite matrix space and generalizations. It is intended for be

This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincare upper half plane. This book is intended for beginning g

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-m

The volume contains the proceedings of the OTAMP 2006 (Operator Theory, Analysis and Mathematical Physics) conference held at Lund University in June 2006. The conference was devoted to the methods of