Format: Paperback / softback, 144 pages, height x width: 235x155 mm, XII, 144 p.
Series: Universitext
Pub. Date: 04-Apr-2023
ISBN-13: 9783031231216
Author Biography
Goodreads reviews
This text provides a concise introduction, suitable for a one-semester special topicscourse, to the remarkable properties of Gaussian measures on both finite and infinitedimensional spaces. It begins with a brief resume of probabilistic results in which Fourieranalysis plays an essential role, and those results are then applied to derive a few basicfacts about Gaussian measures on finite dimensional spaces. In anticipation of the analysisof Gaussian measures on infinite dimensional spaces, particular attention is given to thoseproperties of Gaussian measures that are dimension independent, and Gaussian processesare constructed. The rest of the book is devoted to the study of Gaussian measures onBanach spaces. The perspective adopted is the one introduced by I. Segal and developedby L. Gross in which the Hilbert structure underlying the measure is emphasized.The contents of this book should be accessible to either undergraduate or graduatestudents who are interested in probability theory and have a solid background in Lebesgueintegration theory and a familiarity with basic functional analysis. Although the focus ison Gaussian measures, the book introduces its readers to techniques and ideas that haveapplications in other contexts.
Preface.-
1. Characteristic Functions.-
2. Gaussian Measures and Families.-
3. Gaussian Measures on a Banach Space.-
4. Further Properties and Examples of Abstract Wiener Spaces.- References.- Index.
Format: Hardback, 435 pages, height x width: 235x155 mm, 93 Tables, color; 93 Illustrations,
color; 21 Illustrations, black and white; XV, 435 p. 114 illus., 93 illus. in color.
Pub. Date: 26-Feb-2023
ISBN-13: 9783031226861
This book presents recent developments in multivariate and robust statistical methods. Featuring contributions by leading experts in the field it covers various topics, including multivariate and high-dimensional methods, time series, graphical models, robust estimation, supervised learning and normal extremes. It will appeal to statistics and data science researchers, PhD students and practitioners who are interested in modern multivariate and robust statistics. The book is dedicated to David E. Tyler on the occasion of his pending retirement and also includes a review contribution on the popular Tyler’s shape matrix.
Part I About David E. Tyler's Publications.- An Analysis of David E. Tyler's Publication and Coauthor Network.- A review of Tyler's shape matrix and its extensions.- Part II Multivariate Theory and Methods.- On the asymptotic behavior of the leading eigenvector of Tyler's shape estimator under weak identifiability.- On Minimax Shrinkage Estimation with Variable Selection.- On the Finite-Sample Performance of Measure-Transportation-Based Multivariate Rank Tests.- Refining Invariant Coordinate Selection via Local Projection Pursuit.- Directional distributions and the half-angle principle.- Part III Robust Theory and Methods.- Power M-estimators for Location and Scatter.- On robust estimators of a sphericity measure in high-dimension.- Detecting outliers in compositional data using Invariant Coordinate Selection.- Robust Forecasting of Multiple Time Series with One-Sided Dynamic Principal Components.- Robust and sparse estimation of graphical models based on multivariate Winsorization.- Robustly fitting Gaussian graphical models - the R-package robFitConGraph.- Robust Estimation of General Linear Mixed Effects Models.- Asymptotic behaviour of penalized robust estimators in logistic regression when dimension increases.- Conditional distribution-based down weighting for robust estimation of logistic regression models.- Bias Calibration for Robust Estimation in Small Areas.- The Diverging Definition of Robustness in Statistics and Computer Vision.- Part IV Other Methods.- Power Calculations and Critical Values for Two-Stage Nonparametric Testing Regimes.- Data Nuggets in Supervised Learning.- Improved Convergence Rates of Normal Extremes.- Local Spectral Analysis of Qualitative Sequences via Minimum Description Length.
Format: Hardback, 350 pages, height x width: 235x155 mm, 7 Tables, color; 9 Illustrations, color;
4 Illustrations, black and white; X, 350 p. 13 illus., 9 illus. in color.
Series: Operator Theory: Advances and Applications 290
Pub. Date: 02-Feb-2023
ISBN-13: 9783031214592
This book features a collection of papers by plenary, semi-plenary and invited contributors at IWOTA2021, held at Chapman University in hybrid format in August 2021. The topics span areas of current research in operator theory, mathematical physics, and complex analysis.
Infinite order differential operators with a glimpse to applications to super oscillations.- Interpolation in multivariable de Branges-Rovnyak spaces.- Monotonicity of certain left and right Riemann sums.- A survey on the recent advances in the spectral theory on the S-spectrum.- Stochastics and dynamics of fractals.- Fluid-Plate interaction with Kelvin-Voigt damping and bending moment at the interface: Wellposedness, Spectral Analysis, Uniform Stability.- Automorphisms of Hyper-Reinhardt Free Spectrahedra.- Arithmetic and Analysis of the series, Part II.- Lipschitz-type bounds for functions of operators with noncompact perturbations.- Extended Fock space formalism and polyanalytic functions.- Estimates of Cauchy-Szegoe kernel in Hardy Spaces on Nilpotent Lie Groups of Step Two.
Format: Hardback, 972 pages, height x width: 235x155 mm, 1 Illustrations, color; XVIII, 972 p. 1 illus. in color
Series: Developments in Mathematics 74
Pub. Date: 13-Apr-2023
ISBN-13: 9783031227349
This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. Volume III is concerned with integral representation formulas for nullsolutions of elliptic PDEs, Calderon-Zygmund theory for singular integral operators, Fatou type theorems for systems of elliptic PDEs, and applications to acoustic and electromagnetic scattering. Overall, this amounts to a powerful and nuanced theory developed on uniformly rectifiable sets, which builds on the work of many predecessors.
Introduction and Statement of Main Results Concerning the Divergence Theorem.- Examples, Counterexamples, and Additional Perspectives.- Tools from Geometric Measure Theory, Harmonic Analysis, and functional Analysis.- Open Sets with Locally Finite Surface Measures and Boundary Behavior.- Proofs of the Main Results Pertaining to the Divergence Theorem.- Applications to Singular Integrals, Function Spaces, Boundary Problems, and Further Results.
Format: Hardback, height x width: 240x168 mm, Approx. 340 p., 1 Hardback
Pub. Date: 18-Apr-2023
ISBN-13: 9783031213069
This textbook focuses on the basics and complex themes of group theory taught to senior undergraduate mathematics students across universities. The contents focus on the properties of groups, subgroups, cyclic groups, permutation groups, cosets and Lagrange’s theorem, normal subgroups and factor groups, group homomorphisms and isomorphisms, automorphisms, direct products, group actions and Sylow theorems. Pedagogical elements such as end of chapter exercises and solved problems are included to help understand abstract notions. Intermediate lemmas are also carefully designed so that they not only serve the theorems but are also valuable independently. The book is a useful reference to undergraduate and graduate students besides academics.
Format: Hardback, 658 pages, height x width: 240x168 mm, X, 658 p., 1 Hardback
Pub. Date: 02-Apr-2023
ISBN-13: 9783031213205
This book is designed to meet the requirement of undergraduate and postgraduate students pursuing computer science, information technology, mathematical science, and physical science course. No formal prerequisites are needed to understand the text matter except a very reasonable background in college algebra. The text contains in-depth coverage of all major topics proposed by professional institutions and universities for a discrete mathematics course. It emphasizes on problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof technique, algorithmic development, algorithm correctness, and numeric computations. A sufficient amount of theory is included for those who enjoy the beauty in development of the subject and a wealth of applications as well as for those who enjoy the power of problem-solving techniques.
Biographical sketches of nearly 25 mathematicians and computer scientists who have played a significant role in the development of the field are threaded into the text to provide a human dimension and attach a human face to major discoveries. Each section of the book contains a generous selection of carefully tailored examples to classify and illuminate various concepts and facts. Theorems are backbone of mathematics. Consequently, this book contains the various proof techniques, explained and illustrated in details. Most of the concepts, definitions, and theorems in the book are illustrated with appropriate examples. Proofs shed additional light on the topic and enable students to sharpen thin problem-solving skills. Each chapter ends with a summary of important vocabulary, formulae, properties developed in the chapter, and list of selected references for further exploration and enrichment.
Format: Hardback, height x width: 240x168 mm, Approx. 300 p., 1 Hardback
Pub. Date: 18-Apr-2023
ISBN-13: 9783031225611
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Description
The present book is based on the curriculum of undergraduate and postgraduate courses of universities in India and abroad. Every effort is made to present the various topics in the theory of graphs in a logical manner with adequate historical background and include suitable figures to illustrate concepts and results ideally. The formidable exercises, neither easy nor straightforward, are bold faced and highlighted. The theory portion of each chapter is studied thoroughly as it helps solve many of the problems with comparative ease. Selected material from this book is used for a semester course on graph theory, while the entire book serves for a whole session course.