Books in the Studies in Advanced Mathematics series

Offers a collection of extended survey papers addressing key topics in the mathematical foundations and applications of wavelet theory. This book is suitable for a general scientific and engineering audience, harmonic analysts, partial differential equation researchers, signal processing engineers, numerical analysts, and applied mathematicians.

Harmonic analysis plays an essential role in understanding a host of engineering, mathematical, and scientific ideas. Harmonic Analysis and Applications presents the analysis and synthesis of functions in terms of harmonics in a way that clearly demonstrates the vitality, power, elegance, usefulness of the subject.

The book focuses on describing the geometry of a real hypersurface in a complex vector space by understanding its relationship with ambient complex analytic varieties. Several Complex Variables and the Geometry of Real Hypersurfaces will be a useful text for advanced graduate students and professionals working in complex analysis.

Presents an introduction to wavelet analysis. This book explains the subject using algebra and some basic calculus, and stresses applications, such as speech compression, removing noise from audio and images, image compression, and image enhancement.

Covers a range of information from basic facts about holomorphic functions of several complex variables through deep results such as subelliptic estimates for the Neumann problem on pseudoconvex domains with an analytic boundary. This book is suitable for advanced graduate students and professionals working in complex analysis.

Focuses on material useful to control specialists working in the disciplines of electrical, mechanical, and aerospace engineering. This book offers an introduction to the abstract basic function spaces and operators, then studies problems in the Hilbert space setting.

Offers an elementary introduction to CR manifolds and the tangential Cauchy-Riemann Complex and presents some of the most important recent developments in the field. This book covers the basic definitions and background material concerning CR manifolds, CR functions, the tangential Cauchy-Riemann Complex and the Levi form.

Through synthesis of the achievements since the 1970s and bringing into focus the outlines of the developing theory, this book offers an introduction to the linear operators of composition with a fixed function acting on a space of analytic functions.

Focuses on the fundamental results in operator algebras. This work discusses results including Gelfand's representation of commutative C*-algebras, the GNS construction, the spectral theorem, polar decomposition, von Neumann's double commutant theorem, Kaplansky's density theorem and the functional calculus for normal operators.

Presenting an array of new topics, "Mathematical Quantization" explores operator algebras. For graduate students, this text offers an introduction to a large area of active research, and for professionals in operating algebras and functional analysis, it provides a tour of the field.

Offers an introduction to three related subjects: differential geometry, differential topology, and dynamical systems. This book addresses topics such as Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. It also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models.

Treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. This work also uses heat equation methods to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary.

Presents a survey of intrinsic techniques and practical implementation of higher-order finite element schemes. This book addresses automatic hp-adaptivity in one and two spatial dimensions. It includes a discussion of suitable data structures and efficient linear solvers. It is suitable for both applied mathematicians and engineers.

Offers an examination of the central assertions of measure theory in n-dimensional Euclidean space and emphasizes the roles of Hausdorff measure and the capacity in characterizing the find properties of sets and functions. This book includes proofs of various key results omitted from other books, including Besicovitch's covering theorem.

Offers an introduction to the basic properties of wavelets, from background math to powerful applications. This book provides elementary methods for constructing wavelets, and illustrates several classes of wavelets. It offers a description of local sine and cosine bases that have been shown to be very effective in applications.

A bestselling text and reference in its first edition, Wavelets and Other Orthogonal Systems, Second Edition was fully updated and expanded to reflect the phenomenal growth and development of this field, especially in the area of multiwavelets. The authors incorporated more examples and numerous illustrations to help clarify concepts. They also added a considerable amount of new material, including sections addressing impulse trains, an alternate approach to periodic wavelets, and positive wavelets. Other discussions new to this edition address irregular sampling in wavelet subspaces, hybrid wavelet sampling, interpolating multiwavelets, and several additional statistics topics.

Offers a treatment of Fourier Series, Fourier Transforms, and FFTs. This title covers topics such as applications to vibrating strings, heat conduction, removal of noise and frequency detection, and filtering of Fourier Series and improvement of convergence.

Harmonic analysis plays an essential role in understanding a host of engineering, mathematical, and scientific ideas. Harmonic Analysis and Applications presents the analysis and synthesis of functions in terms of harmonics in a way that clearly demonstrates the vitality, power, elegance, usefulness of the subject.

Shows the phenomenal growth and development of the field of wavelets, especially in the area of multiwavelets. This title contains examples and various illustrations to help clarify concepts. This title includes sections addressing impulse trains, an alternate approach to periodic wavelets, and positive wavelets.

Treats the dynamics of both iteration of functions and solutions of ordinary differential equations. This book introduces various concepts for iteration of functions where the geometry is simpler, but results are interpreted for differential equations. It concentrates on properties of the whole system or subsets of the system.

Presents an introduction to wavelet analysis. This book explains the subject using algebra and some basic calculus, and stresses applications, such as speech compression, removing noise from audio and images, image compression, and image enhancement.