Basic Methods of Linear Functional Analysis

" An introduction to the themes of mathematical analysis, this text is geared toward advanced undergraduate and graduate students. Topics include operators, function spaces, Hilbert spaces, and elemen

This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimens

Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis

This book is an introduction to basic functional analysis and operator theory, with an emphasis on Hilbert space methods. The main aim is to develop rigorously the basic notions of functional analysis

This book was written for students of mathematics and physics who have a basic knowledge of analysis and linear algebra. It can be used as a textbook for courses and/or seminars in functional analysis

Details the basic theory of polynomial and fractional representation methods for algebraic analysis and synthesis of linear multivariable control systems. It also serves as a self-contained treatise o

Facebook and Conversation Analysis investigates the structure and organization of comments on a major social media platform, Facebook, using applied conversation analysis methods. Providing previously

Statistical Design and Analysis of Clinical Trials: Principles and Methods concentrates on the biostatistics component of clinical trials. Developed from the authors’ courses taught to public health a

A concise introduction to the major concepts of functional analysis Requiring only a preliminary knowledge of elementary linear algebra and real analysis, A First Course in Functional Analysis provid

Functional analysis provides a concise conceptual framework for linear control theory. This self-contained text, geared toward engineering students, demonstrates the subject's unity. A wide range of p

This text is designed both for students of probability and stochastic processes, and for students of functional analysis. For the reader not familiar with functional analysis a detailed introduction to necessary notions and facts is provided. However, this is not a straight textbook in functional analysis; rather, it presents some chosen parts of functional analysis that can help understand ideas from probability and stochastic processes. The subjects range from basic Hilbert and Banach spaces, through weak topologies and Banach algebras, to the theory of semigroups of bounded linear operators. Numerous standard and non-standard examples and exercises make the book suitable as a course textbook or for self-study.

This text is designed both for students of probability and stochastic processes, and for students of functional analysis. For the reader not familiar with functional analysis a detailed introduction to necessary notions and facts is provided. However, this is not a straight textbook in functional analysis; rather, it presents some chosen parts of functional analysis that can help understand ideas from probability and stochastic processes. The subjects range from basic Hilbert and Banach spaces, through weak topologies and Banach algebras, to the theory of semigroups of bounded linear operators. Numerous standard and non-standard examples and exercises make the book suitable as a course textbook or for self-study.

This text is a basic course in functional analysis for senior undergraduate and beginning postgraduate students. It aims at providing some insight into basic abstract analysis which is now the contextual language of much modern mathematics. Although it is assumed that the student will have familiarity with elementary real and complex analysis and linear algebra and have studied a course in the analysis of metric spaces, a knowledge of integration theory or general topology is not required. The theme of this text concerns structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. But the implications of the general theory are illustrated with a great variety of example spaces.

The first part of a self-contained, elementary textbook, combining linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with eac

The field of forensic DNA analysis has grown immensely in the past two decades and genotyping of biological samples is now routinely performed in human identification (HID) laboratories. Application areas include paternity testing, forensic casework, family lineage studies, identification of human remains, and DNA databasing. Forensic DNA Analysis: Current Practices and Emerging Technologies explores the fundamental principles and the application of technologies for each aspect of forensic DNA analysis. The book begins by discussing the value of DNA evidence and how to properly recognize, document, collect, and store it. The remaining chapters examine: The most widely adopted methods and the best practices for DNA isolation from forensic biological samples and human remainsStudies carried out on the use of both messenger RNA and small (micro) RNA profilingReal-time polymerase chain reaction (PCR) methods for quantification and assessment of human DNA prior to genotypingCapillary electr

An essential undergraduate textbook on algebra, topology, and calculusAn Introduction to Analysis is an essential primer on basic results in algebra, topology, and calculus for undergraduate students

This two-volume text provides a complete overview of the theory of Banach spaces, emphasising its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. The authors give a full exposition of all results, as well as numerous exercises and comments to complement the text and aid graduate students in functional analysis. The book will also be an invaluable reference volume for researchers in analysis. Volume 1 covers the basics of Banach space theory, operatory theory in Banach spaces, harmonic analysis and probability. The authors also provide an annex devoted to compact Abelian groups. Volume 2 focuses on applications of the tools presented in the first volume, including Dvoretzky's theorem, spaces without the approximation property, Gaussian processes, and more. In volume 2, four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.

Valuation and Risk Management in Energy Markets surveys the mechanics of energy markets and the valuation of structures commonly arising in practice. The presentation balances quantitative issues and practicalities facing portfolio managers, with substantial attention paid to the ways in which common methods fail in practice and to alternative methods when they exist. The material spans basic fundamentals of markets, statistical analysis of price dynamics, and a sequence of increasingly challenging structures, concluding with issues arising at the enterprise level. In totality, the material has been selected to provide readers with the analytical foundation required to function in modern energy trading and risk management groups.

This book focuses on the various functional properties and potential applications of one-dimensional ZnO nanostructures, from basic principles to our most recent discoveries. It comprises experimental

This graduate-level text gives a self-contained exposition of fundamental topics in equilibrium and nonequilibrium statistical thermodynamics. The text follows a balanced approach between the macroscopic (thermodynamic) and microscopic (statistical) points of view. The first half of the book deals with equilibrium thermodynamics and statistical mechanics. In addition to standard subjects, the reader will find a detailed account of broken symmetries, critical phenomena and the renormalization group, as well as an introduction to numerical methods. The second half of the book is devoted to nonequilibrium phenomena, first following a macroscopic approach, with hydrodynamics as an important example. Kinetic theory receives a thorough treatment through analysis of the Boltzmann-Lorentz model and the Boltzmann equation. The book concludes with general nonequilibrium methods such as linear response, projection method and the Langevin and Fokker-Planck equations, including numerical simulation

This book provides a concise and meticulous introduction to functional analysis. Since the topic draws heavily on the interplay between the algebraic structure of a linear space and the distance struc

This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.

This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.

This book provides a concise and meticulous introduction to functional analysis. Since the topic draws heavily on the interplay between the algebraic structure of a linear space and the distance struc

This book provides a broad overview of the basic theory and methods of applied multivariate analysis. The presentation integrates both theory and practice including both the analysis of formal linear

This book provides a broad overview of the basic theory and methods of applied multivariate analysis. The presentation integrates both theory and practice including both the analysis of formal linear

A unique introduction to the theory of linear operators on Hilbert space. The author presents the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathemati

This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis an

Use real data, and become a pro at using Excel for statistical analysis! Designed for users already familiar with Excel and basic computer operations, this Second Edition of Neil J. Salkind’s Excel St

The new 6th edition of Applied Combinatorics builds on the previous editions with more in depth analysis of computer systems in order to help develop proficiency in basic discrete math problem solving

This book gives an introduction to Linear Functional Analysis, a synthesis of algebra, topology, and analysis. In addition to the basic theory it explains operator theory, distributions, Sobolev space

This book offers a brief, practically complete, and relatively simple introduction to functional analysis. It also illustrates the application of functional analytic methods to the science of continuu

Vath (Freie U. Berlin) introduces topology, functional analysis, and analysis for advanced readers who have taken a first course in analysis and are adept in basic calculus and linear algebra. He also

The main goal of this book is to introduce readers to functional analysis methods, in particular, time dependent analysis, for reliability models. Understanding the concept of reliability is of key im

Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a

Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces th

This set features: Linear Algebra and Its Applications, Second Edition (978-0-471-75156-4) and Functional Analysis (978-0-471-55604-6) both by Peter D. Lax.

A comprehensive graduate textbook that introduces functional analysis with an emphasis on the theory of linear operators and its application to differential equations, integ

The unifying approach of functional analysis is to view functions as points in some abstract vector space and the differential and integral operators relating these points as linear transformations o

Introductory text covers basic structures of mathematical analysis (linear spaces, metric spaces, normed linear spaces, etc.), differential equations, orthogonal expansions, Fourier transforms — inclu