Theoretical Foundations Of Functional Data Analysis With An Introduction To Linear Operators

Author : Tailen Hsing,Randall Eubank
Publisher : John Wiley & Sons
Page : 368 pages
File Size : 48,8 Mb
Release : 2015-04-07
Category : Mathematics
ISBN : 9781118762578

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Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators by Tailen Hsing,Randall Eubank Pdf

Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.

Author : V. Hutson,J. Pym,M. Cloud
Publisher : Elsevier
Page : 432 pages
File Size : 48,6 Mb
Release : 2005-02-08
Category : Mathematics
ISBN : 9780080527314

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Applications of Functional Analysis and Operator Theory by V. Hutson,J. Pym,M. Cloud Pdf

Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces. Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results Introduces each new topic with a clear, concise explanation Includes numerous examples linking fundamental principles with applications Solidifies the reader's understanding with numerous end-of-chapter problems

Author : James Ramsay,B. W. Silverman
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 46,9 Mb
Release : 2006-06-28
Category : Mathematics
ISBN : 9780387227511

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Functional Data Analysis by James Ramsay,B. W. Silverman Pdf

This is the second edition of a highly succesful book which has sold nearly 3000 copies world wide since its publication in 1997. Many chapters will be rewritten and expanded due to a lot of progress in these areas since the publication of the first edition. Bernard Silverman is the author of two other books, each of which has lifetime sales of more than 4000 copies. He has a great reputation both as a researcher and an author. This is likely to be the bestselling book in the Springer Series in Statistics for a couple of years.

Author : Lajos Horváth,Piotr Kokoszka
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 40,8 Mb
Release : 2012-05-08
Category : Mathematics
ISBN : 9781461436553

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Inference for Functional Data with Applications by Lajos Horváth,Piotr Kokoszka Pdf

This book presents recently developed statistical methods and theory required for the application of the tools of functional data analysis to problems arising in geosciences, finance, economics and biology. It is concerned with inference based on second order statistics, especially those related to the functional principal component analysis. While it covers inference for independent and identically distributed functional data, its distinguishing feature is an in depth coverage of dependent functional data structures, including functional time series and spatially indexed functions. Specific inferential problems studied include two sample inference, change point analysis, tests for dependence in data and model residuals and functional prediction. All procedures are described algorithmically, illustrated on simulated and real data sets, and supported by a complete asymptotic theory. The book can be read at two levels. Readers interested primarily in methodology will find detailed descriptions of the methods and examples of their application. Researchers interested also in mathematical foundations will find carefully developed theory. The organization of the chapters makes it easy for the reader to choose an appropriate focus. The book introduces the requisite, and frequently used, Hilbert space formalism in a systematic manner. This will be useful to graduate or advanced undergraduate students seeking a self-contained introduction to the subject. Advanced researchers will find novel asymptotic arguments.

Author : James Ramsay,B. W. Silverman
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 47,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475771077

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Functional Data Analysis by James Ramsay,B. W. Silverman Pdf

Included here are expressions in the functional domain of such classics as linear regression, principal components analysis, linear modelling, and canonical correlation analysis, as well as specifically functional techniques such as curve registration and principal differential analysis. Data arising in real applications are used throughout for both motivation and illustration, showing how functional approaches allow us to see new things, especially by exploiting the smoothness of the processes generating the data. The data sets exemplify the wide scope of functional data analysis; they are drawn from growth analysis, meteorology, biomechanics, equine science, economics, and medicine. The book presents novel statistical technology while keeping the mathematical level widely accessible. It is designed to appeal to students, applied data analysts, and to experienced researchers; and as such is of value both within statistics and across a broad spectrum of other fields. Much of the material appears here for the first time.

Author : Piotr Kokoszka,Matthew Reimherr
Publisher : CRC Press
Page : 311 pages
File Size : 42,8 Mb
Release : 2017-09-27
Category : Mathematics
ISBN : 9781498746694

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Introduction to Functional Data Analysis by Piotr Kokoszka,Matthew Reimherr Pdf

Introduction to Functional Data Analysis provides a concise textbook introduction to the field. It explains how to analyze functional data, both at exploratory and inferential levels. It also provides a systematic and accessible exposition of the methodology and the required mathematical framework. The book can be used as textbook for a semester-long course on FDA for advanced undergraduate or MS statistics majors, as well as for MS and PhD students in other disciplines, including applied mathematics, environmental science, public health, medical research, geophysical sciences and economics. It can also be used for self-study and as a reference for researchers in those fields who wish to acquire solid understanding of FDA methodology and practical guidance for its implementation. Each chapter contains plentiful examples of relevant R code and theoretical and data analytic problems. The material of the book can be roughly divided into four parts of approximately equal length: 1) basic concepts and techniques of FDA, 2) functional regression models, 3) sparse and dependent functional data, and 4) introduction to the Hilbert space framework of FDA. The book assumes advanced undergraduate background in calculus, linear algebra, distributional probability theory, foundations of statistical inference, and some familiarity with R programming. Other required statistics background is provided in scalar settings before the related functional concepts are developed. Most chapters end with references to more advanced research for those who wish to gain a more in-depth understanding of a specific topic.

Author : Daniel Alpay,Maria Elena Luna-Elizarrarás,Michael Shapiro,Daniele C. Struppa
Publisher : Springer Science & Business Media
Page : 95 pages
File Size : 46,8 Mb
Release : 2014-03-19
Category : Mathematics
ISBN : 9783319051109

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Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis by Daniel Alpay,Maria Elena Luna-Elizarrarás,Michael Shapiro,Daniele C. Struppa Pdf

This book provides the foundations for a rigorous theory of functional analysis with bicomplex scalars. It begins with a detailed study of bicomplex and hyperbolic numbers and then defines the notion of bicomplex modules. After introducing a number of norms and inner products on such modules (some of which appear in this volume for the first time), the authors develop the theory of linear functionals and linear operators on bicomplex modules. All of this may serve for many different developments, just like the usual functional analysis with complex scalars and in this book it serves as the foundational material for the construction and study of a bicomplex version of the well known Schur analysis.

Author : Kösaku Yosida
Publisher : Springer Science & Business Media
Page : 517 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642618598

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Functional Analysis by Kösaku Yosida Pdf

The present book is based on lectures given by the author at the University of Tokyo during the past ten years. It is intended as a textbook to be studied by students on their own or to be used in a course on Functional Analysis, i. e. , the general theory of linear operators in function spaces together with salient features of its application to diverse fields of modern and classical analysis. Necessary prerequisites for the reading of this book are summarized, with or without proof, in Chapter 0 under titles: Set Theory, Topo logical Spaces, Measure Spaces and Linear Spaces. Then, starting with the chapter on Semi-norms, a general theory of Banach and Hilbert spaces is presented in connection with the theory of generalized functions of S. L. SOBOLEV and L. SCHWARTZ. While the book is primarily addressed to graduate students, it is hoped it might prove useful to research mathe maticians, both pure and applied. The reader may pass, e. g. , from Chapter IX (Analytical Theory of Semi-groups) directly to Chapter XIII (Ergodic Theory and Diffusion Theory) and to Chapter XIV (Integration of the Equation of Evolution). Such materials as "Weak Topologies and Duality in Locally Convex Spaces" and "Nuclear Spaces" are presented in the form of the appendices to Chapter V and Chapter X, respectively. These might be skipped for the first reading by those who are interested rather in the application of linear operators.

Author : Anuj Srivastava,Eric P. Klassen
Publisher : Springer
Page : 447 pages
File Size : 52,8 Mb
Release : 2016-10-03
Category : Mathematics
ISBN : 9781493940202

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Functional and Shape Data Analysis by Anuj Srivastava,Eric P. Klassen Pdf

This textbook for courses on function data analysis and shape data analysis describes how to define, compare, and mathematically represent shapes, with a focus on statistical modeling and inference. It is aimed at graduate students in analysis in statistics, engineering, applied mathematics, neuroscience, biology, bioinformatics, and other related areas. The interdisciplinary nature of the broad range of ideas covered—from introductory theory to algorithmic implementations and some statistical case studies—is meant to familiarize graduate students with an array of tools that are relevant in developing computational solutions for shape and related analyses. These tools, gleaned from geometry, algebra, statistics, and computational science, are traditionally scattered across different courses, departments, and disciplines; Functional and Shape Data Analysis offers a unified, comprehensive solution by integrating the registration problem into shape analysis, better preparing graduate students for handling future scientific challenges. Recently, a data-driven and application-oriented focus on shape analysis has been trending. This text offers a self-contained treatment of this new generation of methods in shape analysis of curves. Its main focus is shape analysis of functions and curves—in one, two, and higher dimensions—both closed and open. It develops elegant Riemannian frameworks that provide both quantification of shape differences and registration of curves at the same time. Additionally, these methods are used for statistically summarizing given curve data, performing dimension reduction, and modeling observed variability. It is recommended that the reader have a background in calculus, linear algebra, numerical analysis, and computation.

Author : Israel Gohberg,Mark Grigorʹevich Kreĭn
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 42,5 Mb
Release : 1978
Category : Mathematics
ISBN : 0821886509

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Introduction to the Theory of Linear Nonselfadjoint Operators by Israel Gohberg,Mark Grigorʹevich Kreĭn Pdf

Author : Erwin Kreyszig
Publisher : John Wiley & Sons
Page : 706 pages
File Size : 50,9 Mb
Release : 1991-01-16
Category : Mathematics
ISBN : 9780471504597

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Introductory Functional Analysis with Applications by Erwin Kreyszig Pdf

KREYSZIG The Wiley Classics Library consists of selected books originally published by John Wiley & Sons that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: Emil Artin Geometnc Algebra R. W. Carter Simple Groups Of Lie Type Richard Courant Differential and Integrai Calculus. Volume I Richard Courant Differential and Integral Calculus. Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics. Volume II Harold M. S. Coxeter Introduction to Modern Geometry. Second Edition Charles W. Curtis, Irving Reiner Representation Theory of Finite Groups and Associative Algebras Nelson Dunford, Jacob T. Schwartz unear Operators. Part One. General Theory Nelson Dunford. Jacob T. Schwartz Linear Operators, Part Two. Spectral Theory—Self Adjant Operators in Hilbert Space Nelson Dunford, Jacob T. Schwartz Linear Operators. Part Three. Spectral Operators Peter Henrici Applied and Computational Complex Analysis. Volume I—Power Senes-lntegrauon-Contormal Mapping-Locatvon of Zeros Peter Hilton, Yet-Chiang Wu A Course in Modern Algebra Harry Hochstadt Integral Equations Erwin Kreyszig Introductory Functional Analysis with Applications P. M. Prenter Splines and Variational Methods C. L. Siegel Topics in Complex Function Theory. Volume I —Elliptic Functions and Uniformizatton Theory C. L. Siegel Topics in Complex Function Theory. Volume II —Automorphic and Abelian Integrals C. L. Siegel Topics In Complex Function Theory. Volume III —Abelian Functions & Modular Functions of Several Variables J. J. Stoker Differential Geometry

Author : Christian Clason
Publisher : Springer Nature
Page : 166 pages
File Size : 48,9 Mb
Release : 2020-11-30
Category : Mathematics
ISBN : 9783030527846

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Introduction to Functional Analysis by Christian Clason Pdf

Functional analysis has become one of the essential foundations of modern applied mathematics in the last decades, from the theory and numerical solution of differential equations, from optimization and probability theory to medical imaging and mathematical image processing. This textbook offers a compact introduction to the theory and is designed to be used during one semester, fitting exactly 26 lectures of 90 minutes each. It ranges from the topological fundamentals recalled from basic lectures on real analysis to spectral theory in Hilbert spaces. Special attention is given to the central results on dual spaces and weak convergence.

Author : Kendall Atkinson,Weimin Han
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 53,5 Mb
Release : 2001-03-09
Category : Mathematics
ISBN : 9780387951423

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Theoretical Numerical Analysis by Kendall Atkinson,Weimin Han Pdf

This book gives an introduction to functional analysis in a way that is tailored to fit the needs of the researcher or student. The book explains the basic results of functional analysis as well as relevant topics in numerical analysis. Applications of functional analysis are given by considering numerical methods for solving partial differential equations and integral equations. The material is especially useful for researchers and students who wish to work in theoretical numerical analysis and seek a background in the "tools of the trade" covered in this book.

Author : Svetlin G. Georgiev,Khaled Zennir
Publisher : Walter de Gruyter GmbH & Co KG
Page : 524 pages
File Size : 41,7 Mb
Release : 2019-06-17
Category : Mathematics
ISBN : 9783110658040

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Functional Analysis with Applications by Svetlin G. Georgiev,Khaled Zennir Pdf

This book on functional analysis covers all the basics of the subject (normed, Banach and Hilbert spaces, Lebesgue integration and spaces, linear operators and functionals, compact and self-adjoint operators, small parameters, fixed point theory) with a strong focus on examples, exercises and practical problems, thus making it ideal as course material but also as a reference for self-study.

Author : Arlen Brown,Carl M. Pearcy
Publisher : Unknown
Page : 128 pages
File Size : 43,8 Mb
Release : 1977
Category : Operator theory
ISBN : 7506200856

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Introduction to Operator Theory: Elements of functional analysis by Arlen Brown,Carl M. Pearcy Pdf