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. |
Contents
Preface | 1 |
Linear Algebra | 123 |
Linear Transformations | 157 |
Algebraic Duals | 185 |
Euclidean Spaces | 205 |
Lebesgue Measure and Integration | 215 |
Lebesgue Integration Theory | 248 |
LP Spaces | 282 |
Topological and Metric Spaces | 289 |
Banach Spaces | 383 |
HahnBanach Extension Theorem | 398 |
Hilbert Spaces | 511 |
| 643 | |
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Common terms and phrases
a₁ accumulation point adjoint algebraic arbitrary axioms b₁ ball Banach space bijective bilinear Borel bounded called Cartesian product Cauchy sequence closed sets compact set complete Consequently consider continuous functions converges COROLLARY corresponding countable d(xn definition denote dense domain dual eigenvalues element equations equivalence classes equivalence relation Example Exercises exists finite finite-dimensional spaces function defined function f Hilbert space identified implies inequality infinite inner product inner product space integral inverse isomorphism Lemma Let f lim inf linear and continuous linear functional linear operator linear transformation linearly independent mapping matrix metric space nonempty normed space notion Obviously open sets orthogonal PROOF Proposition prove quotient space real numbers representation respect scalar self-adjoint seminorm sequentially compact solution subset subspace surjective tensor theorem topological space topology transpose unique vector space