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$a(EXLCZ)993400000000089284 100 $a20121227d1995 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aApplied Functional Analysis$b[electronic resource] $eMain Principles and Their Applications /$fby Eberhard Zeidler 205 $a1st ed. 1995. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1995. 215 $a1 online resource (XVI, 406 p.) 225 1 $aApplied Mathematical Sciences,$x0066-5452 ;$v109 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-94422-2 311 $a1-4612-6913-X 320 $aIncludes bibliographical references and index. 327 $a1 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 ?eby?ev 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. 330 $aA theory is the more impressive, the simpler are its premises, the more distinct are the things it connects, and the broader is its range of applicability. Albert Einstein There are two different ways of teaching mathematics, namely, (i) the systematic way, and (ii) the application-oriented way. More precisely, by (i), I mean a systematic presentation of the material governed by the desire for mathematical perfection and completeness of the results. In contrast to (i), approach (ii) starts out from the question "What are the most important applications?" and then tries to answer this question as quickly as possible. Here, one walks directly on the main road and does not wander into all the nice and interesting side roads. The present book is based on the second approach. It is addressed to undergraduate and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems that are related to our real world and that have played an important role in the history of mathematics. The reader should sense that the theory is being developed, not simply for its own sake, but for the effective solution of concrete problems. viii Preface Our introduction to applied functional analysis is divided into two parts: Part I: Applications to Mathematical Physics (AMS Vol. 108); Part II: Main Principles and Their Applications (AMS Vol. 109). A detailed discussion of the contents can be found in the preface to AMS Vol. 108. 410 0$aApplied Mathematical Sciences,$x0066-5452 ;$v109 606 $aFunctional analysis 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aSystem theory 606 $aCalculus of variations 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 615 0$aFunctional analysis. 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 0$aSystem theory. 615 0$aCalculus of variations. 615 14$aFunctional Analysis. 615 24$aAnalysis. 615 24$aSystems Theory, Control. 615 24$aCalculus of Variations and Optimal Control; Optimization. 676 $a515.7 686 $a46Bxx$2msc 700 $aZeidler$b Eberhard$4aut$4http://id.loc.gov/vocabulary/relators/aut$040565 906 $aBOOK 912 $a9910789342603321 996 $aApplied functional analysis$983422 997 $aUNINA LEADER 03287nam 22006014a 450 001 9910784631603321 005 20230120005119.0 010 $a1-280-63045-0 010 $a9786610630455 010 $a0-08-045418-6 035 $a(CKB)1000000000384808 035 $a(EBL)269861 035 $a(OCoLC)475999814 035 $a(SSID)ssj0000082309 035 $a(PQKBManifestationID)11125399 035 $a(PQKBTitleCode)TC0000082309 035 $a(PQKBWorkID)10136297 035 $a(PQKB)11433298 035 $a(MiAaPQ)EBC269861 035 $a(Au-PeEL)EBL269861 035 $a(CaPaEBR)ebr10138163 035 $a(CaONFJC)MIL63045 035 $a(EXLCZ)991000000000384808 100 $a20050329d2005 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aRivers of North America$b[electronic resource] /$fedited by Arthur C. 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Cushing 210 $aAmsterdam ;$aBoston $cElsevier/Academic Press$dc2005 215 $a1 online resource (1168 p.) 300 $aDescription based upon print version of record. 311 $a1-84972-346-X 311 $a0-12-088253-1 320 $aIncludes bibliographical references. 327 $aCONTRIBUTORS; FOREWORD; PREFACE; ACKNOWLEDGMENTS; 1: BACKGROUND AND APPROACH; 2: ATLANTIC COAST RIVERS OF THE NORTHEASTERN UNITED STATES; 3: ATLANTIC COAST RIVERS OF THE SOUTHEASTERN United STATES; 4: GULF COAST RIVERS OF THE SOUTHEASTERN UNITED STATES; 5: GULF COAST RIVERS OF THE SOUTHWESTERN UNITED STATES; 6: LOWER MISSISSIPPI RIVER AND ITS TRIBUTARIES; 7: SOUTHERN PLAINS RIVERS; 8: UPPER MISSISSIPPI RIVER BASIN; 9: OHIO RIVER BASIN; 10: MISSOURI RIVER BASIN; 11: COLORADO RIVER BASIN; 12: PACIFIC COAST RIVERS OF THE COTERMINOUS UNITED STATES; 13: COLUMBIA RIVER BASIN; 14: GREAT BASIN RIVERS 327 $a15: FRASER RIVER basin16: PACIFIC COAST RIVERS OF CANADA AND ALASKA; 17: YUKON RIVER BASIN; 18: MACKENZIE RIVER BASIN; 19: NELSON AND CHURCHILL RIVER BASINS; 20: RIVERS OF ARCTIC NORTH AMERICA; 21: ATLANTIC COAST RIVERS OF CANADA; 22: ST. LAWRENCE RIVER BASIN; 23: RIVERS OF MEXICO; 24: OVERVIEW AND PROSPECTS; APPENDIX: COMMON AND SCIENTIFIC NAMES FOR PLANTS, VERTEBRATES, AND SELECTED INVERTEBRATES; GLOSSARY; INDEX OF RIVERS 330 $aAWARDS:2006 Outstanding Academic Title, by CHOICEThe 2005 Award for Excellence in Professional and Scholarly Publishing by the Association of American Publishers (AAP) Best Reference 2005, by the Library JournalRivers of North America is an important reference for scientists, ecologists, and students studying rivers and their ecosystems. It brings together information from several regional specialists on the major river basins of North America, presented in a large-format, full-color book. The introduction covers general aspects of geolog 606 $aRivers$zNorth America 606 $aStream ecology$zNorth America 615 0$aRivers 615 0$aStream ecology 676 $a551.48/3 701 $aBenke$b Arthur C$01560626 701 $aCushing$b C. 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