Books in the CBMS Regional Conference Series in Mathematics series

The concept of 'wave packet analysis' originates in Carleson's famous proof of almost everywhere convergence of Fourier series of $L^2$ functions. This work emphasizes the classical successes (Carleson's theorem and the Hilbert transform) in the main development.

Surveys some of the remarkable developments that have taken place in operator theory over the years. This monograph is largely expository and should be accessible to those who have had a course in functional analysis and operator theory.

In this book on smooth and non-smooth harmonic analysis, the notion of dual variables is adapted to fractals. In addition to harmonic analysis via Fourier duality, the author also covers multiresolution wavelet approaches as well as a third tool, namely, $L^2$ spaces derived from appropriate Gaussian processes.

Tensors are used throughout the sciences, especially in solid state physics and quantum information theory. This book brings a geometric perspective to the use of tensors in these areas. Numerous open problems appropriate for graduate students and post-docs are included throughout.

Systems of polynomial equations can be used to model an astonishing variety of phenomena. This book explores the geometry and algebra of such systems and includes numerous applications.

Includes an analytic solution to the Busemann-Petty problem, which asks whether bodies with smaller areas of central hyperplane sections necessarily have smaller volume, characterizations of intersection bodies, extremal sections of certain classes of bodies, and a Fourier analytic solution to Shephard's problem on projections of convex bodies.

Examines some recent developments in the theory of $C^*$-algebras, which are algebras of operators on Hilbert spaces. An elementary introduction to the technical part of the theory is given via a basic homotopy lemma concerning a pair of almost commuting unitaries.

Considers models that are described by systems of partial differential equations, focusing on modelling rather than on numerical methods and simulations. The models studied are concerned with population dynamics, cancer, risk of plaque growth associated with high cholesterol, and wound healing.

Zeta and $L$-functions play a central role in number theory. They provide important information of arithmetic nature. This book, which grew out of the author's teaching over several years, explores the interaction between number theory and combinatorics using zeta and $L$-functions as a central theme.

Provides introductory material to give the reader an accessible entry point to this vast subject matter. Instead of technical theorems or complete proofs, the book relies on providing essential points of many arguments through explicit examples, with the hope that they will be useful for applied mathematicians and physicists.

Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The emphasis is on the global methods and the use of Fourier integral operator methods to analyse norms and nodal sets of eigenfunctions.