**Best Reference Books on Functional Analysis**, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of

**Functional Analysis Books**with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Functional Analysis below.

## 1. Functional Analysis

1."Introduction to Topology and Modern Analysis" by G F Simmons
“Introduction to Topology and Modern Analysis” Book Review: This book extensively covers the mathematical aspects of continuity and linearity. After explaining their basic definition, the book explores their relationship to each other in terms of topology and modern analysis. Students, researchers, and professionals can refer to this book.
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2."Functional Analysis" by G Bachman and L Narici
“Functional Analysis” Book Review: This book introduces the inner-product spaces, normed and metric spaces, and topological spaces in great detail. Complete orthonormal sets, the Hahn-Banach theorem and its consequences are also covered. Subsequent chapters deal with spectral notions, square roots, a spectral decomposition theorem, etc. Detailed proofs of theorems, definitions, index of symbols, and end-of-chapter exercises are also included. Students with background in linear algebra, advanced calculus, physics and engineering can refer to this book.
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3."Introduction to Functional Analysis" by A E Taylor
“Introduction to Functional Analysis” Book Review: This book includes the basic principles of functional analysis. This book systematically analyzes the theory of normed linear spaces and linear mappings between such spaces. Separate chapters on Banach algebras, the Krein-Milman theorem, weak topologies and duality, equicontinuity, and the theory of Fredholm operators provided. Recent advances in functional analysis are also included with special focus on closed unbounded linear operators. The unifying power of the abstract linear-space is studied using problems of linear algebra, classical analysis, and differential and integral equations. Illustrations are drawn from ordinary differential equations. This book can be referred to by graduate students of mathematics.
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4."Functional Analysis" by B V Limaye
“Functional Analysis” Book Review: This book is divided into two sections and introduces a distance structure on a linear space with additional features. The first section covers normed spaces, their completeness and continuous linear maps on them including the theory of compact operators. Meanwhile, the second section deals with Hilbert spaces and spectral theorems for compact self-adjoint operators. Numerous examples and problems of varying levels of difficulty are provided to illustrate abstract concepts and applications of results. The approximate construction of a solution is also indicated along with its existence and uniqueness.
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5."Introductory Functional Analysis with Applications" by Erwin Kreyszig
“Introductory Functional Analysis with Applications” Book Review: This book explores the application of functional analysis to the practical study of natural sciences and mathematics. The book concentrates on the fundamental concepts, principles, methods, and major applications of functional analysis. Numerous problems on Hilbert space theory and Banach spaces are also solved in this text to provide a better understanding of the subject.
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6."Functional Analysis" by P K Jain
“Functional Analysis” Book Review: This book introduces the fundamentals of real analysis, linear algebra, and metric spaces along with the uniform notations in the initial chapters. This is followed by discussions on normed and Banach spaces, bounded linear operators and bounded linear functionals. Subsequent chapters deal with the theory and specific geometry of Hilbert spaces, functionals and operators on Hilbert spaces. Separate chapters on spectral theory and Schauder bases are also included. This book is designed for senior undergraduate- and graduate-level students.
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7."Functional Analysis: A First Course" by Nair
“Functional Analysis” Book Review: The book presents a concise treatment of functional analysis using various figures and examples. After discussing linear algebra and linear space, the book introduces operators and some basic theorems of functional analysis. Advanced topics like dual space considerations, compact operators, and spectral theory of Banach and Hilbert space operators are also addressed. The theorems are then applied and related to problems which arise while solving operator equations. This book is ideal for the postgraduate students in Mathematics.
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8."Functional Analysis" by Walter Rudin
“Functional Analysis” Book Review: This book presents a modern take of functional analysis from the analysis and applied mathematics perspective. Advanced topics like Lamonosov’s invariant subspace theorem, Kakutani’s fixed point theorem, and an ergodic theorem are also explained in detail. Replete with examples and exercises, this text is suitable for graduate courses in functional analysis.
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9."Textbook of Functional Analysis: A Problem-Oriented Approach" by Krishnan V K
“Textbook of Functional Analysis” Book Review: This book explains and demonstrates the use of the fundamental theorems in functional analysis through solved numerical problems in a comprehensive manner. Solved numerical problems related to the spectral properties of compact operators on Banach spaces and Hilbert spaces are also included for thorough practice. Problems based on the square root of a positive operator are also provided along with exercise sets for the readers to solve. This is a suitable book for students pursuing postgraduate courses in mathematics.
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10."Functional Analysis, Sobolev Spaces and Partial Differential Equations (Universitext)" by Haim Brezis
“Functional Analysis, Sobolev Spaces and Partial Differential Equations (Universitext)” Book Review: This book is designed for students of mathematics, physics, and engineering from all branches. The book mainly focuses on functional analysis (FA) and partial differential equations (PDEs). It includes dimensional PDEs, representation of modern theory. It also includes The analysis of numerical schemes based on Fourier techniques, maximum principles, and Lax’s theorem. This book is intended for students who have a good background in real analysis. Later it focuses on applied mathematics, appearing in linear and nonlinear PDEs. The book contains a large number of solved examples and practice exercises.
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## 2. Computational Functional Analysis

1."Computational Functional Analysis" by Ramon E Moore and Michael J Cloud
“Computational Functional Analysis” Book Review: This book discusses the topics regarding advanced engineering analysis and modern control theory. Main topics mentioned are linear spaces, topological spaces, matrix spaces, normed linear spaces and banach spaces. Other chapters included are inner product spaces and Hilbert spaces, linear functional, types of convergence in functional spaces, order relation in function spaces. Over 100 problems and exercises are discussed in this book with complete solutions. Answers and tutorial hints for students are provided at the end of the book. students studying applied functional analysis can refer to this book.
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2."An Introduction to Functional Analysis in Computational Mathematics" by V I Lebedev
“An Introduction to Functional Analysis in Computational Mathematics” Book Review: This book provides the basics of function analysis and the methods used in computational mathematics. Main chapters included are functional spaces and problems in the theory of approximation, linear operators and functional, iteration methods for the solution of operator equations. Other topics included are The Newton method, partial Eigenvalue problem, spaces of linear operators and linear spaces. All the properties and equations are described in detail with proper explanations. theorems and methods are provided with figures and descriptive explanations. This book is beneficial for students studying functional analysis.
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3."Introductory Functional Analysis: With Applications to Boundary Value Problems and Finite Elements (Texts in Applied Mathematics)" by B D Reddy
“Introductory Functional Analysis: With Applications to Boundary Value Problems and Finite Elements (Texts in Applied Mathematics)” Book Review: This book explains the basics of functional analysis. Main topics included are boundary value problems, finite element method, real analysis and its applications. all the applications and problem statements about boundary value and finite element method discussed in detail with proper examples. This book is useful for graduates in mathematics, physical science and engineering students.
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4."Functional Analysis and Applications" by imusti | |

5."Real and Functional Analysis (Mathematical Concepts and Methods in Science and Engineering)" by imusti | |

6."Introduction to Measure Theory and Functional Analysis" by Piermarco Cannarsa and Teresa D'Aprile
“Introduction to Measure Theory and Functional Analysis” Book Review: This book describes the main concept of measure theory and function analysis. Main topics mentioned are measure spaces, integration, product measures, Hilbert spaces. Other topics included are banach spaces, signed measures, absolute continuous functions, set value functions. Miscellaneous examples and exercises are provided at the end of each unit. References are also mentioned at the end of each chapter for further reading purposes. All the theorems and methods are described in a detailed manner. This book is useful for graduate students in mathematics.
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7."Applications of Methods of Functional Analysis to Problems in Mechanics" by P Germain and B Nayroles
“Applications of Methods of Functional Analysis to Problems in Mechanics” Book Review: This book discusses the applications of methods of functional analysis to the problems faced in mechanics. various papers are provided in this book which were presented at a joint symposium of IUTAM/IMU held in Marseille in 1975. topics included in equation quasi vibrational problems, the alliance of practical and analytical insights into the nonlinear problems of fluid mechanics, applications of convex analysis to the treatment of elasto plastic systems. A total of 44 chapters are mentioned in this book. This book is useful for advanced mathematics and research students.
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8."Computational Text Analysis: For Functional Genomics and Bioinformatics" by Soumya Raychaudhuri
“Computational Text Analysis: For Functional Genomics and Bioinformatics” Book Review: This book discusses the important topics on computational text analysis and functional genomics. Main chapters included are sequence analysis, gene expansion data, applications to proteomics complex functions and interactions. Practical examples and modern experiments are provided in this book for students. This book is useful for students and researchers in the field of computational biology, bioinformatics and computer science.
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## 3. Nonlinear Functional Analysis

1."Nonlinear Functional Analysis: A First Course (Texts and Readings in Mathematics)" by S Kesavan | |

2."An Introduction to Nonlinear Functional Analysis and Elliptic Problems (Progress in Nonlinear Differential Equations and Their Applications)" by Antonio Ambrosetti and David Arcoya Álvarez
“An Introduction to Nonlinear Functional Analysis and Elliptic Problems (Progress in Nonlinear Differential Equations and Their Applications)” Book Review: This book presents the basic, abstract tools used in nonlinear analysis. It also discusses their applications to semilinear elliptic boundary value problems. This book provides information on how various approaches can easily be applied to a range of model cases. It includes further results on weak derivatives. This book also avails chapter-end exercises. It serves as a practical text for an introductory course or seminar on nonlinear functional analysis.
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3."Linear and Nonlinear Functional Analysis with Applications" by Philippe G Ciarlet
“Linear and Nonlinear Functional Analysis with Applications” Book Review: This book provides a thorough and complete introduction to the basic aspects of linear and nonlinear functional analysis. It presents complete proofs, and illustrations with various applications to numerical analysis. It also includes optimisation theory, and partial differential equations. This book covers a large amount of foundational material, historical notes. It also provides several original references to help us explore the genesis of some important results. This book serves the advanced undergraduates, graduate students, and researchers.
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4."Nonlinear Functional Analysis and Its Applications (Nato Science Series C:)" by S P Singh
“Nonlinear Functional Analysis and Its Applications (Nato Science Series C:)” Book Review: This book provides the proceedings of the institute. These proceedings contain lectures and contributed papers given during the Institute. These lectures focus on bringing together recent and up-to-date development of the subject. These also give directions for future research. This book covers degree and generalized degree theory, results related to Hamiltonian Systems. It also presents Fixed Point theory, linear and nonlinear Differential and Partial Differential Equations. It also includes Theory of Nielsen Numbers, and applications to Dynamical Systems, Bifurcation Theory. This book covers Hamiltonian Systems, Minimax Theory, Heat Equations, Pendulum Equation, Nonlinear Boundary Value Problems.
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5."Nonlinear Functional Analysis" by Klaus Deimling
“Nonlinear Functional Analysis” Book Review: This book provides extensive commentary. It presents several examples along with plenty of interesting, challenging exercises. This book covers the development of the Brower degree and its applications. It moves to examinations of degree mappings for infinite dimensional spaces and surveys. These surveys are of monotone and accretive mappings. This book also explores the inverse function theory, implicit function theory, and Newton’s methods.
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6."Nonlinear Functional Analysis (American Mathematics Society non-series title)" by Rajendra Akerkar | |

7."Nonlinear Functional Analysis: 121 (Lecture Notes in Pure and Applied Mathematics)" by P S Milojevic | |

8."Spectral Theory and Nonlinear Functional Analysis" by Julian Lopez-Gomez
“Spectral Theory and Nonlinear Functional Analysis” Book Review: This book provides several pivotal problems in spectral theory. It presents nonlinear functional analysis. These are provided in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. This book covers the construction of an optimal algebraic/analytic invariant. This is used for calculating the Leray-Schauder degree. It discusses new methods for solving nonlinear equations in Banach spaces. This book covers general properties of components of solutions sets presented with minimal use of topological tools.
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9."Delay Equations: Functional-, Complex-, and Nonlinear Analysis (Applied Mathematical Sciences)" by Odo Diekmann and Hans-Otto Walther
“Delay Equations: Functional-, Complex-, and Nonlinear Analysis (Applied Mathematical Sciences)” Book Review: This book provides an introduction to the mathematical theory of infinite dimensional dynamical systems. This is done by focusing on a nearly simple – yet rich – class of examples, delay differential equations. It presents detailed proofs and many exercises. These are intended both for self-study and for courses at graduate level. This book can also be used as a reference for basic results. This book provides the working knowledge of applied functional analysis and dynamical systems.
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10."Functional Analysis" by K Yoshida
“Functional Analysis” Book Review: The book begins with a presentation on set theory, topological spaces, measure spaces, and linear spaces. Moving on to Semi-norms, a general theory of Banach and Hilbert spaces and the theory of generalized functions is clearly presented. The chapters feature analytical theory of semi-groups, ergodic theory and diffusion theory, integration of the equation of evolution, weak topologies, and duality in locally convex spaces and nuclear spaces. The applications of functional analysis in various fields of modern and classical analysis are highlighted in this book. The book is basically for the graduating students of mathematics but will be equally important for the researchers related to pure and applied mathematics.
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11."First Course in Functional Analysis" by G Goffman and G Pedrick | |

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