## Applied Functional Analysis, Second EditionFunctional analysis-the study of the properties of mathematical functions-is widely used in modern scientific and engineering disciplines, particularly in mathematical modeling and computer simulation. Applied Functional Analysis, the only textbook of its kind, is designed specifically for the graduate student in engineering and science who has little or no training in advanced mathematics. Comprehensive and easy-to-understand, this innovative textbook progresses from the essentials of preparatory mathematics to sophisticated functional analysis. This self-contained presentation requires few mathematical prerequisites and provides students with the fundamental concepts and theorems essential to mathematical analysis and modeling. Applied Functional Analysis combines various principles of mathematics, computer science, engineering, and science, laying the foundation for further specialty work in partial differential equations, approximation theory, numerical mathematics, control theory, mathematical physics, and related subjects. This new treatment of a classic subject outfits engineering and science majors with a graduate-level mathematics standing, otherwise accessible only through regular mathematics studies. |

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Its a very well-written book. Nothing is left to imagination in his style of explanation. Topics covered are not very usual ones, but clarity of these seemingly unimportant and obvious facts take one towards a proper understanding of the subject such as functional analysis.

### Contents

Preliminaries | 1 |

Linear Algebra | 123 |

Lebesgue Measure and Integration | 215 |

Topological and Metric Spaces | 289 |

Banach Spaces | 383 |

Hilbert Spaces | 511 |

Duality in Hilbert Spaces | 556 |

643 | |

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### Common terms and phrases

accumulation point adjoint algebraic arbitrary assume axioms ball Banach space base of neighborhoods bijective bilinear Borel bounded called Cartesian product Cauchy sequence closed sets compact set complete complex numbers Consequently consider contains continuous functional converges COROLLARY corresponding countable cr-algebra definition denote dense domain dual eigenvalues element equations equivalence classes equivalence relation Example Exercises exists finite finite-dimensional spaces formula fundamental Hilbert space identified implies inequality infinite inner product space integral inverse isomorphism Lebesgue measurable Lemma linear and continuous linear functional linear operator linear transformation linearly independent matrix metric space nonempty normed space notion Obviously open sets partition Proposition prove quotient space real numbers reflexive representation respect Riemann right-hand side satisfies scalar self-adjoint seminorm sequentially compact solution Step subset subspace surjective tensor theorem topological space topology transpose unique vector space