# Applied Functional Analysis: Main Principles and Their Applications

## Zeidler, Eberhard

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The second part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, and their substantial applications. The book addresses undergraduates and beginning graduates of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world and which play an important role in the history of mathematics. The books approach is to attempt to determine the most important applications. These concern integral equations, differential equations, bifurcation theory, the moment problem, Cebysev approximation, the optimal control of rockets, game theory, symmetries and conservation laws, the quark model, and gauge theory in elementary particle physics. The presentation is self-contained and requires only that readers be familiar with some basic facts of calculus.

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Contenuti:

1 The Hahn-Banach Theorem Optimization Problems.- 1.1 The Hahn-Banach Theorem.- 1.2 Applications to the Separation of Convex Sets.- 1.3 The Dual Space C[a,b]*.- 1.4 Applications to the Moment Problem.- 1.5 Minimum Norm Problems and Duality Theory.- 1.6 Applications to ?ebyšev Approximation.- 1.7 Applications to the Optimal Control of Rockets.- 2 Variational Principles and Weak Convergence.- 2.1 The nth Variation.- 2.2 Necessary and Sufficient Conditions for Local Extrema and the Classical Calculus of Variations.- 2.3 The Lack of Compactness in Infinite-Dimensional Banach Spaces.- 2.4 Weak Convergence.- 2.5 The Generalized Weierstrass Existence Theorem.- 2.6 Applications to the Calculus of Variations.- 2.7 Applications to Nonlinear Eigenvalue Problems.- 2.8 Reflexive Banach Spaces.- 2.9 Applications to Convex Minimum Problems and Variational Inequalities.- 2.10 Applications to Obstacle Problems in Elasticity.- 2.11 Saddle Points.- 2.12 Applications to Duality Theory.- 2.13 The von Neumann Minimax Theorem on the Existence of Saddle Points.- 2.14 Applications to Game Theory.- 2.15 The Ekeland Principle about Quasi-Minimal Points.- 2.16 Applications to a General Minimum Principle via the Palais-Smale Condition.- 2.17 Applications to the Mountain Pass Theorem.- 2.18 The Galerkin Method and Nonlinear Monotone Operators.- 2.19 Symmetries and Conservation Laws (The Noether Theorem).- 2.20 The Basic Ideas of Gauge Field Theory.- 2.21 Representations of Lie Algebras.- 2.22 Applications to Elementary Particles.- 3 Principles of Linear Functional Analysis.- 3.1 The Baire Theorem.- 3.2 Application to the Existence of Nondifferentiable Continuous Functions.- 3.3 The Uniform Boundedness Theorem.- 3.4 Applications to Cubature Formulas.- 3.5 The Open Mapping Theorem.- 3.6 Product Spaces.- 3.7 The Closed Graph Theorem.- 3.8 Applications to Factor Spaces.- 3.9 Applications to Direct Sums and Projections.- 3.10 Dual Operators.- 3.11 The Exactness of the Duality Functor.- 3.12 Applications to the Closed Range Theorem and to Fredholm Alternatives.- 4 The Implicit Function Theorem.- 4.1 m-Linear Bounded Operators.- 4.2 The Differential of Operators and the Fréchet Derivative.- 4.3 Applications to Analytic Operators.- 4.4 Integration.- 4.5 Applications to the Taylor Theorem.- 4.6 Iterated Derivatives.- 4.7 The Chain Rule.- 4.8 The Implicit Function Theorem.- 4.9 Applications to Differential Equations.- 4.10 Diffeomorphisms and the Local Inverse Mapping Theorem.- 4.11 Equivalent Maps and the Linearization Principle.- 4.12 The Local Normal Form for Nonlinear Double Splitting Maps.- 4.13 The Surjective Implicit Function Theorem.- 4.14 Applications to the Lagrange Multiplier Rule.- 5 Fredholm Operators.- 5.1 Duality for Linear Compact Operators.- 5.2 The Riesz-Schauder Theory on Hilbert Spaces.- 5.3 Applications to Integral Equations.- 5.4 Linear Fredholm Operators.- 5.5 The Riesz-Schauder Theory on Banach Spaces.- 5.6 Applications to the Spectrum of Linear Compact Operators.- 5.7 The Parametrix.- 5.8 Applications to the Perturbation of Fredholm Operators.- 5.9 Applications to the Product Index Theorem.- 5.10 Fredholm Alternatives via Dual Pairs.- 5.11 Applications to Integral Equations and Boundary-Value Problems.- 5.12 Bifurcation Theory.- 5.13 Applications to Nonlinear Integral Equations.- 5.14 Applications to Nonlinear Boundary-Value Problems.- 5.15 Nonlinear Fredholm Operators.- 5.16 Interpolation Inequalities.- 5.17 Applications to the Navier-Stokes Equations.- References.- List of Symbols.- List of Theorems.- List of Most Important Definitions.

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## 1.Applied Functional Analysis: Main Principles and Their Applications (Applied Mathematical Sciences)

Editore: Springer (1995)
ISBN 10: 0387944222 ISBN 13: 9780387944227
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Descrizione libro Springer, 1995. Hardcover. Condizione libro: New. FAST SHIPPING & FREE TRACKING! 100% Money Back Guaranteed. The pages of this book are clean and unmarked. There is very little shelf wear. The spine is solid and the binding is tight. Codice libro della libreria 132695

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## 2.Applied Functional Analysis: Main Principles and Their Applications (Hardback)

Editore: Springer-Verlag New York Inc., United States (1995)
ISBN 10: 0387944222 ISBN 13: 9780387944227
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Descrizione libro Springer-Verlag New York Inc., United States, 1995. Hardback. Condizione libro: New. 1995 ed.. 236 x 163 mm. Language: English . Brand New Book. The second part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, and their substantial applications. The book addresses undergraduates and beginning graduates of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world and which play an important role in the history of mathematics. The books approach is to attempt to determine the most important applications. These concern integral equations, differential equations, bifurcation theory, the moment problem, Cebysev approximation, the optimal control of rockets, game theory, symmetries and conservation laws, the quark model, and gauge theory in elementary particle physics. The presentation is self-contained and requires only that readers be familiar with some basic facts of calculus. Codice libro della libreria LIB9780387944227

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## 3.Applied Functional Analysis: Main Principles and Their Applications (Hardback)

Editore: Springer-Verlag New York Inc., United States (1995)
ISBN 10: 0387944222 ISBN 13: 9780387944227
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Descrizione libro Springer-Verlag New York Inc., United States, 1995. Hardback. Condizione libro: New. 1995 ed.. 236 x 163 mm. Language: English . Brand New Book. The second part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, and their substantial applications. The book addresses undergraduates and beginning graduates of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world and which play an important role in the history of mathematics. The books approach is to attempt to determine the most important applications. These concern integral equations, differential equations, bifurcation theory, the moment problem, Cebysev approximation, the optimal control of rockets, game theory, symmetries and conservation laws, the quark model, and gauge theory in elementary particle physics. The presentation is self-contained and requires only that readers be familiar with some basic facts of calculus. Codice libro della libreria LIB9780387944227

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## 4.Applied Functional Analysis

Editore: Springer-Verlag New York Inc. 1995-08-30, New York, NY (1995)
ISBN 10: 0387944222 ISBN 13: 9780387944227
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Descrizione libro Springer-Verlag New York Inc. 1995-08-30, New York, NY, 1995. hardback. Condizione libro: New. Codice libro della libreria 9780387944227

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## 5.Applied Functional Analysis. Main Principles and Their Applications

Editore: Springer (1995)
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Descrizione libro Springer, 1995. Hardback. Condizione libro: NEW. 9780387944227 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0275430

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## 6.Applied Functional Analysis

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## 7.Applied Functional Analysis. Main Principles and Their Applications

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Descrizione libro 1995. Condizione libro: New. Codice libro della libreria L9780387944227

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## 8.Applied Functional Analysis

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## 9.Applied Functional Analysis : Main Principles and Their Applications

Editore: Springer (2016)
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Descrizione libro Springer, 2016. Paperback. Condizione libro: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice libro della libreria ria9780387944227_lsuk

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## 10.Applied Functional Analysis. Main Principles and Their Applications

Editore: Springer-Verlag Gmbh Jan 1995 (1995)
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