ISBN: 978-1-119-71213-8
February 2025
416 pages
Comprehensive textbook examining meaningful connections between the subjects of Lie theory, differential geometry, and signal analysis
A Bridge Between Lie Theory and Frame Theory serves as a bridge between the areas of Lie theory, differential geometry, and frame theory, illustrating applications in the context of signal analysis with concrete examples and images.
The first part of the book gives an in-depth, comprehensive, and self-contained exposition of differential geometry, Lie theory, representation theory, and frame theory. The second part of the book uses the theories established in the early part of the text to characterize a class of representations of Lie groups, which can be discretized to construct frames and other basis-like systems. For instance, Lie groups with frames of translates, sampling, and interpolation spaces on Lie groups are characterized.
A Bridge Between Lie Theory and Frame Theory includes discussion on:
Novel constructions of frames possessing additional desired features such as boundedness, compact support, continuity, fast decay, and smoothness, motivated by applications in signal analysis
Necessary technical tools required to study the discretization problem of representations at a deep level
Ongoing dynamic research problems in frame theory, wavelet theory, time frequency analysis, and other related branches of harmonic analysis
A Bridge Between Lie Theory and Frame Theory is an essential learning resource for graduate students, applied mathematicians, and scientists who are looking for a rigorous and complete introduction to the covered subjects.
Hardcover
ISBN: 9780262049399
Pub date: November 5, 2024
672 pp., 7 x 10 in, 97 b&w illus.
A comprehensive, cutting-edge, and highly readable textbook that makes category theory and monoidal category theory accessible to students across the sciences.
Category theory is a powerful framework that began in mathematics but has since expanded to encompass several areas of computing and science, with broad applications in many fields. In this comprehensive text, Noson Yanofsky makes category theory accessible to those without a background in advanced mathematics. Monoidal Category Theory demonstrates the expansive uses of categories, and in particular monoidal categories, throughout the sciences. The textbook starts from the basics of category theory and progresses to cutting-edge research. Each idea is defined in simple terms and then brought alive by many real-world examples before advancing to theorems and uncomplicated proofs. Richly guided exercises ground readers in concrete computation and application. The result is a highly readable and engaging textbook that will open the world of category theory to many.
? Makes category theory accessible to non-math majors
? Uses easy-to-understand language and emphasizes diagrams over equations
? Incremental, iterative approach eases students into advanced concepts
? A series of embedded mini-courses cover such popular topics as quantum computing, categorical logic, self-referential paradoxes, databases and scheduling, and knot theory
? Extensive exercises and examples demonstrate the broad range of applications of categorical structures
? Modular structure allows instructors to fit text to the needs of different courses
? Instructor resources include slides
Features new and original research that expands upon Stochastic Limit Theory: An Introduction to Econometricians
Provides accessible material for students of econometrics and statistics
Covers a range of topics
Asymptotics for Fractional Processes develops an approach to the large-sample analysis of fractional partial-sum processes, featuring long memory increments. Long memory in a time series, equivalently called strong dependence, is usually defined to mean that the autocovariance sequence is non-summable. The processes studied have a linear moving average representation with a single parameter, denoted d, to measure the degree of long-run persistence. Long memory means that d is positive, while negative d defines a special type of short memory known as antipersistence in which the autocovariance sequence sums to zero. Antipersistent processes are treated in parallel with the long memory case.
This book features the weak convergence of normalized partial sums to fractional Brownian motion and the limiting distribution of stochastic integrals where both the integrand and the integrator processes exhibit either long memory or antipersistence. It also covers applications to cointegration analysis and the treatment of dependent shock processes and includes chapters on the harmonic analysis of fractional models and local-to-unity autoregression.
1:The Fractional Model
2:Fractional Asymptotics
3:The FCLT for Fractional Processes
4:The Fractional Covariance
5:Stochastic Integrals
6:Weak Convergence of Integrals
7:Fractional Cointegration
8:Autocorrelated Shocks
9:Frequency Domain Analysis
10:Autoregressive Roots near Unity
A: Appendix: Useful Results
B: Appendix: Identities and Integral Solutions
References
Index
Important lectures on differential topology by acclaimed mathematician John Milnor
Hardcover
ISBN: 9780691273730
Mar 25, 2025
Pages:122
6.13 x 9.25 in.
Overview
These are notes from lectures that John Milnor delivered as a seminar on differential topology in 1963 at Princeton University. These lectures give a new proof of the h-cobordism theorem that is different from the original proof presented by Stephen Smale. Milnorfs goal was to provide a fully rigorous proof in terms of Morse functions. This book remains an important resource in the application of Morse theory.
Awards and Recognition
John Milnor, Winner of the 2011 Abel Prize from the Norwegian Academy of Science and Letters
John Willard Milnor, Winner of the 2011 Leroy P. Steele Prize for Lifetime Achievement, American Mathematical Society