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Elements of the Theory of Functions and Functional Analysis
Originally published in two volumes, this advanced-level text is based on courses and lectures given by the authors at Moscow State University and the University of Moscow.
Reprinted here in one volume, the first part is devoted to metric and normal spaces. Beginning with a brief introduction to set theory and mappings, the authors offer a clear presentation of the theory of metric and complete metric spaces. The principle of contraction mappings and its applications to the proof of existence theorems in the theory of differential and integral equations receives detailed analysis, as do continuous curves in metric spaces — a topic seldom discussed in textbooks.
Part One also includes discussions of other subjects, such as elements of the theory of normed linear spaces, weak sequential convergence of elements and linear functionals, adjoint operators, and linear operator equations. Part Two focuses on an exposition of measure theory, the Lebesque interval and Hilbert Space. Both parts feature numerous exercises at the end of each section and include helpful lists of symbols, definitions, and theorems.
Reprinted here in one volume, the first part is devoted to metric and normal spaces. Beginning with a brief introduction to set theory and mappings, the authors offer a clear presentation of the theory of metric and complete metric spaces. The principle of contraction mappings and its applications to the proof of existence theorems in the theory of differential and integral equations receives detailed analysis, as do continuous curves in metric spaces — a topic seldom discussed in textbooks.
Part One also includes discussions of other subjects, such as elements of the theory of normed linear spaces, weak sequential convergence of elements and linear functionals, adjoint operators, and linear operator equations. Part Two focuses on an exposition of measure theory, the Lebesque interval and Hilbert Space. Both parts feature numerous exercises at the end of each section and include helpful lists of symbols, definitions, and theorems.
One-volume reprint of the two-volume edition published by the Graylock Press, Rochester, New York, 1957.
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Originally published in two volumes, this advanced-level text is based on courses and lectures given by the authors at Moscow State University and the University of Moscow.
Reprinted here in one volume, the first part is devoted to metric and normal spaces. Beginning with a brief introduction to set theory and mappings, the authors offer a clear presentation of the theory of metric and complete metric spaces. The principle of contraction mappings and its applications to the proof of existence theorems in the theory of differential and integral equations receives detailed analysis, as do continuous curves in metric spaces — a topic seldom discussed in textbooks.
Part One also includes discussions of other subjects, such as elements of the theory of normed linear spaces, weak sequential convergence of elements and linear functionals, adjoint operators, and linear operator equations. Part Two focuses on an exposition of measure theory, the Lebesque interval and Hilbert Space. Both parts feature numerous exercises at the end of each section and include helpful lists of symbols, definitions, and theorems.
Reprinted here in one volume, the first part is devoted to metric and normal spaces. Beginning with a brief introduction to set theory and mappings, the authors offer a clear presentation of the theory of metric and complete metric spaces. The principle of contraction mappings and its applications to the proof of existence theorems in the theory of differential and integral equations receives detailed analysis, as do continuous curves in metric spaces — a topic seldom discussed in textbooks.
Part One also includes discussions of other subjects, such as elements of the theory of normed linear spaces, weak sequential convergence of elements and linear functionals, adjoint operators, and linear operator equations. Part Two focuses on an exposition of measure theory, the Lebesque interval and Hilbert Space. Both parts feature numerous exercises at the end of each section and include helpful lists of symbols, definitions, and theorems.
One-volume reprint of the two-volume edition published by the Graylock Press, Rochester, New York, 1957.
hilbert space;differential equations;functional analysis;measure theory;linear operators;theory background;differential calculus;self study;physics students;mathematical analysis;math student;particular statement;exactly 200;writting style;graduate level;topics range;graduate students;quantum mechanics;graduate school;royden;dunford;fourier;schwartz;lemmas;matrix;trigonometric;cauchy;probability;edwards;integrals;counterexamples;orthogonal;topological;algebra;mendelson;dover;compactness;self-study;topology;equivalence;theorems;axiom;metric;connectedness;mathematics;proofs;undergraduate;proposition;applications;intuition;rigorous;intuitive;definitions;functions;abstract;introductory;exercises;fomin;russian;moscow;books on cauchies;books on mathematical analysis;books on algebras;books on graduate levels;books on differential calculus;books on functional analysis;books on lemmas;books on theorems;books on mendelson;books on matrices;books on theory backgrounds;books on proofs;books on graduate students;books on integrals;books on differential equations;books on self studies;books on axioms;books on edwards;books on topologies;books on math students;books on dovers;books on fourier;books on measure theories;books on mathematics;books on graduate schools;books on probabilities;books on physics students;books on hilbert spaces;books on self-studies;books on linear operators;books on applications;books on schwartz;books on royden;books on writting styles
