Integrates modern and classical shrinkage estimation and contributes to
further developments in the field
Provides a unified approach to low- and high-dimensional models with
respect to the size of the mean matrix
Presents recent results of high-dimensional generalization of decisiontheoretic estimation of the covariance matrix
This book provides a self-contained introduction to shrinkage estimation for matrix-variate
normal distribution models. More specifically, it presents recent techniques and results in
estimation of mean and covariance matrices with a high-dimensional setting that implies
singularity of the sample covariance matrix. Such high-dimensional models can be analyzed by
using the same arguments as for low-dimensional models, thus yielding a unified approach to
both high- and low-dimensional shrinkage estimations. The unified shrinkage approach not
only integrates modern and classical shrinkage estimation, but is also required for further
development of the field. Beginning with the notion of decision-theoretic estimation, this book
explains matrix theory, group invariance, and other mathematical tools for finding better
estimators. It also includes examples of shrinkage estimators for improving standard
estimators, such as least squares, maximum likelihood, and minimum risk invariant estimators,
and discusses the historical background and related topics in decision-theoretic estimation of
parameter matrices. This book is useful for researchers and graduate students in various fields
requiring data analysis skills as well as in mathematical statistics.
Due 2020-07-02
1st ed. 2020, X, 100 p.
Softcover
ISBN 978-981-15-1595-8
Product category : Brief
Series : JSS Research Series in Statistics
Is among the first new books on G2 manifolds in decades
Features introductory lectures on several aspects of G2 geometry by
recognized experts in the field
Serves as an accessible entry point for early career researchers looking to
work in the field
Contains survey articles on numerous recent developments in G2 geometry
and related topics
This book, one of the first on G2 manifolds in decades, collects introductory lectures and
survey articles largely based on talks given at a workshop held at the Fields Institute inAugust
2017, as part of the major thematic program on geometric analysis. It provides an
accessibleintroduction to various aspects of thegeometry of G2 manifolds, including the
construction of examples, as well as the intimaterelations with calibrated geometry, Yang-Mills
gauge theory, and geometric flows. It also featuresthe inclusion of a survey on the new
topological and analytic invariants of G2manifolds that have been recently discovered. The first
half of the book, consisting of several introductory lectures, is aimed at experiencedgraduate
students or early career researchers in geometry and topology who wish to
familiarizethemselves with this burgeoning field. The second half, consisting of numerous
survey articles, isintended to be useful to both beginners and experts in the field
Due 2020-07-11
1st ed. 2020, XX, 322 p.
Hardcover
ISBN 978-1-0716-0576-9
Product category : Contributed volume
Series : Fields Institute Communications
March 2020
Pages: 856
ISBN: 978-981-121-549-0 (hardcover)
ISBN: 978-981-121-633-6 (softcover)
Vol. I: Introductory Calculus, Analysis of Functions of One Real Variable
Vol. II: Differentiation and Integration of Functions of Several Variables, Vector Calculus
Vol. III: Measure and Integration Theory, Complex-Valued Functions of a Complex Variable
Vol. IV: Fourier Analysis, Ordinary Differential Equations, Calculus of Variations
The book is an advanced textbook and a reference text in functional analysis
in the wide sense. It provides advanced undergraduate and graduate students
with a coherent introduction to the field, i.e. the basic principles, and
leads them to more demanding topics such as the spectral theorem, Choquet
theory, interpolation theory, analysis of operator semigroups, Hilbertchmidt
operators and Hilleamarkin operators, topological vector spaces and distribution
theory, fundamental solutions, or the Schwartz kernel theorem.
All topics are treated in great detail and the text provided is suitable for self-studying the subject. This is enhanced by more than 270 problems solved in detail. At the same time the book is a reference text for any working mathematician needing results from functional analysis, operator theory or the theory of distributions.
Embedded as Volume V in the Course of Analysis, readers will have a self-contained treatment of a key area in modern mathematics. A detailed list of references invites to further studies.
Preface
Introduction
List of Symbols
Functional Analysis:
What is Functional Analysis about?
Infinite Dimensional Vector Spaces
Banach Spaces
Linear Operators and Linear Functionals
The Dual Space
The Basic Principles of Functional Analysis
Adjoint Operators and Fredholm Theory
Hilbert Spaces and Operators in Hilbert Spaces
Unbounded Operators in Hilbert Spaces
Spectral Theory. Part I: Gelfandaimark Theory
Spectral Theory. Part II: Self-adjoint Operators
Topological Vector Spaces
Convexity and Integral Representations
Selected Topics
Some Operator Theory:
Some Integral Operators
One-Parameter Semigroups of Operators
Positivity Preserving Operators and Markovian Semigroups
On Regular Sturm-Liouville Problems
Sobolev Spaces. A First Encounter
Operators Induced by the Dirichlet Problem
Selected Topics
Distributions:
Some Function Spaces as Fréchet Spaces
Distributions in the Sense of Schwartz
Further Properties of Distributions
Tempered Distributions and the Fourier Transform
Tensor Products and the Kernel Theorem
Calderon-Zygmund Operators
Appendices:
Completeness
Nets, Convergence and Continuity
On the Riesz Representation Theorem
Solutions to Problems of Part 12
Solutions to Problems of Part 13
Solutions to Problems of Part 14
References
Mathematicians Contributing to Analysis (Continued)
Subject Index
Advanced undergraduate students, graduate students, researchers in analysis.
July 2020
Pages: 300
ISBN: 978-981-121-410-3 (hardcover)
This timely book exposes succinctly recent advances in the geometric and analytic theory of bounded symmetric domains. A unique feature is the unified treatment to both finite and infinite dimensional symmetric domains, using Jordan theory in tandem with Lie theory. The highlights include a generalized Riemann mapping theorem, which realizes a bounded symmetric domain as the open unit ball of a complex Banach space with a Jordan structure. Far-reaching applications of this realization in complex geometry and function theory are discussed. This monograph is intended to be a convenient reference for researchers and graduate students in geometric analysis, infinite dimensional holomorphy as well as functional analysis and operator theory.
Chapter 1:
Holomorphic Maps in Banach Spaces
Banach Manifolds
Symmetric Banach Manifolds
Chapter 2:
Jordan Algebras
Jordan Triple Systems
Lie Algebras and Titsantoroecher Construction
Jordan and Lie Structures in Banach Spaces
Cartan Factors
Chapter 3:
Algebraic Structures of Symmetric Manifolds
Realisation of Bounded Symmetric Domains
Rank of a Bounded Symmetric Domain
Boundary Structures
Invariant Metrics, Schwarz Lemma and Dynamics
Siegel Domains
Homogeneous Regular Domains
Classification
Chapter 4:
The Class S
Bloch Constant and Bloch Maps
Banach Spaces of Bloch Functions
Composition Operators
Graduate students and researchers in diverse mathematical fields including complex geometry, function theory, functional analysis and operator theory. It would also appeal to algebraists who are interested in the applications of Jordan and Lie algebras.