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Operators and Representation Theory
Three-part treatment covers background material on definitions, terminology, operators in Hilbert space domains of representations, operators in the enveloping algebra, spectral theory; and covariant representation and connections. 2017 edition.
Discrete Fourier And Wavelet Transforms: An Introduction Through Linear Algebra With Applications To Signal Processing
This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.
Nilpotent Lie Groups
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A Comprehensive Introduction to Sub-Riemannian Geometry
Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications. For graduate students and researchers.
Multi-parameter Singular Integrals. (AM-189), Volume I
This book develops a new theory of multi-parameter singular integrals associated with Carnot-Carathéodory balls. Brian Street first details the classical theory of Calderón-Zygmund singular integrals and applications to linear partial differential equations. He then outlines the theory of multi-parameter Carnot-Carathéodory geometry, where the main tool is a quantitative version of the classical theorem of Frobenius. Street then gives several examples of multi-parameter singular integrals arising naturally in various problems. The final chapter of the book develops a general theory of singular integrals that generalizes and unifies these examples. This is one of the first general theories of multi-parameter singular integrals that goes beyond the product theory of singular integrals and their analogs. Multi-parameter Singular Integrals will interest graduate students and researchers working in singular integrals and related fields.
Pixels & Paintings
PIXELS & PAINTINGS “The discussion is firmly grounded in established art historical practices, such as close visual analysis and an understanding of artists’ working methods, and real-world examples demonstrate how computer-assisted techniques can complement traditional approaches.” —Dr. Emilie Gordenker, Director of the Van Gogh Museum The pioneering presentation of computer-based image analysis of fine art, forging a dialog between art scholars and the computer vision community In recent years, sophisticated computer vision, graphics, and artificial intelligence algorithms have proven to be increasingly powerful tools in the study of fine art. These methods—some adapted from fore...
Nilpotent Lie Groups
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