Griffel, D. H. Applied Functional Analysis

# Applied Functional Analysis

## Griffel, D. H.

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This introductory text examines many important applications of functional analysis to mechanics, fluid mechanics, diffusive growth, and approximation. Discusses distribution theory, Green's functions, Banach spaces, Hilbert space, spectral theory, and variational techniques. Also outlines the ideas behind Frechet calculus, stability and bifurcation theory, and Sobolev spaces. 1985 edition. Includes 25 figures and 9 appendices. Supplementary problems. Indexes.

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Contenuti:

Preface Part I. Distribution Theory and Green's Functions Chapter 1. Generalised Functions 1.1 The Delta function 1.2 Basic distribution theory 1.3 Operations on distributions 1.4 Convergence of distributions 1.5 Further developments 1.6 Fourier Series and the Poisson Sum formula 1.7 Summary and References Problems Chapter 2. Differential Equations and Green's Functions 2.1 The Integral of a distribution 2.2 Linear differential equations 2.3 Fundamental solutions of differential equations 2.4 Green's functions 2.5 Applications of Green's functions 2.6 Summary and References Problems Chapter 3. Fourier Transforms and Partial differential Equations 3.1 The classical Fourier transform 3.2 Distributions of slow growth 3.3 Generalised Fourier transforms 3.4 Generalised functions of several variables 3.5 Green's function for the Laplacian 3.6 Green's function for the Three-dimensional wave equation 3.7 Summary and References Problems Part II. Banach spaces and fixed point theorems Chapter 4. Normed spaces 4.1 Vector spaces 4.2 Normed spaces 4.3 Convergence 4.4 Open and closed sets 4.5 Completeness 4.6 Equivalent norms 4.7 Summary and References Problems Chapter 5. The contraction mapping theorem 5.1 Operators on Vector spaces 5.2 The contraction mapping theorem 5.3 Application to differential and integral equations 5.4 Nonlinear diffusive equilibrium 5.5 Nonlinear diffusive equilibrium in three dimensions 5.6 Summary and References Problems Chapter 6. Compactness and Schauder's theorem 6.1 Continuous operators 6.2 Brouwer's theorem 6.3 Compactness 6.4 Relative compactness 6.5 Arzelà's theorem 6.6 Schauder's theorems 6.7 Forced nonlinear oscillations 6.8 Swirling flow 6.9 Summary and References Problems Part III. Operators in Hilbert Space Chapter 7. Hilbert space 7.1 Inner product spaces 7.2 Orthogonal bases 7.3 Orthogonal expansions 7.4 The Bessel, Parseval, and Riesz-Fischer theorems 7.5 Orthogonal decomposition 7.6 Functionals on normed spaces 7.7 Functionals in Hilbert space 7.8 Weak convergence 7.9 Summary and References Problems Chapter 8. The Theory of operators 8.1 Bounded operators on normed spaces 8.2 The algebra of bounded operators 8.3 Self-adjoint operators 8.4 Eigenvalue problems for self-adjoint operators 8.5 Compact operators 8.6 Summary and References Problems Chapter 9. The Spectral theorem 9.1 The spectral theorem 9.2 Sturm-Liouville systems 9.3 Partial differential equations 9.4 The Fredholm alternative 9.5 Projection operators 9.6 Summary and References Problems Chapter 10. Variational methods 10.1 Positive operators 10.2 Approximation to the first eigenvalue 10.3 The Rayleigh-Ritz method for eigenvalues 10.4 The theory of the Rayleigh-Ritz method 10.5 Inhomogeneous Equations 10.6 Complementary bounds 10.7 Summary and References Problems Part IV. Further developments Chapter 11. The differential calculus of operators and its applications 11.1 The Fréchet derivative 11.2 Higher derivatives 11.3 Maxima and Minima 11.4 Linear stability theory 11.5. Nonlinear stability 11.6 Bifurcation theory 11.7 Bifurcation and stability 11.8 Summary and References Chapter 12. Distributional Hilbert spaces 12.1 The space of square-integrable distributions 12.2 Sobolev spaces 12.3 Application to partial differential equations 12.4 Summary and References Appendix A. Sets and mappings Appendix B. Sequences, series, and uniform convergence Appendix C. Sup and inf Appendix D. Countability Appendix E. Equivalence relations Appendix F. Completion Appendix G. Sturm-Liouville systems Appendix H. Fourier's theorem Appendix I. Proofs of 9.24 and 9.25 Notes on the Problems; Supplementary Problems; Symbol index; References and name index; Subject index

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## 1.Applied Functional Analysis

Editore: Dover Pubns (2002)
ISBN 10: 0486422585 ISBN 13: 9780486422589
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Descrizione libro Dover Pubns, 2002. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Codice libro della libreria V0-9780486422589

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## 2.Applied Functional Analysis (Paperback)

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Descrizione libro Dover Publications Inc., United States, 2003. Paperback. Condizione libro: New. Reprint. 231 x 155 mm. Language: English . Brand New Book. A stimulating introductory text, this volume examines many important applications of functional analysis to mechanics, fluid mechanics, diffusive growth, and approximation. Detailed enough to impart a thorough understanding, the text is also sufficiently straightforward for those unfamiliar with abs. Codice libro della libreria AAC9780486422589

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## 4.Applied Functional Analysis (Paperback)

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Descrizione libro Dover Publications Inc., United States, 2003. Paperback. Condizione libro: New. Reprint. 231 x 155 mm. Language: English . Brand New Book. A stimulating introductory text, this volume examines many important applications of functional analysis to mechanics, fluid mechanics, diffusive growth, and approximation. Detailed enough to impart a thorough understanding, the text is also sufficiently straightforward for those unfamiliar with abs. Codice libro della libreria AAC9780486422589

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Descrizione libro Dover Publications Inc. Paperback. Condizione libro: new. BRAND NEW, Applied Functional Analysis, D. H. Griffel. Codice libro della libreria B9780486422589

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## 6.Applied Functional Analysis (Dover Books on Mathematics)

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Descrizione libro Dover Publications, 2002. Condizione libro: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: Preface Part I. Distribution Theory and Green's Functions Chapter 1. Generalised Functions 1.1 The Delta function 1.2 Basic distribution theory 1.3 Operations on distributions 1.4 Convergence of distributions 1.5 Further developments 1.6 Fourier Series and the Poisson Sum formula 1.7 Summary and References Problems Chapter 2. Differential Equations and Green's Functions 2.1 The Integral of a distribution 2.2 Linear differential equations 2.3 Fundamental solutions of differential equations 2.4 Green's functions 2.5 Applications of Green's functions 2.6 Summary and References Problems Chapter 3. Fourier Transforms and Partial differential Equations 3.1 The classical Fourier transform 3.2 Distributions of slow growth 3.3 Generalised Fourier transforms 3.4 Generalised functions of several variables 3.5 Green's function for the Laplacian 3.6 Green's function for the Three-dimensional wave equation 3.7 Summary and References Problems Part II. Banach spaces and fixed point theorems Chapter 4. Normed spaces 4.1 Vector spaces 4.2 Normed spaces 4.3 Convergence 4.4 Open and closed sets 4.5 Completeness 4.6 Equivalent norms 4.7 Summary and References Problems Chapter 5. The contraction mapping theorem 5.1 Operators on Vector spaces 5.2 The contraction mapping theorem 5.3 Application to differential and integral equations 5.4 Nonlinear diffusive equilibrium 5.5 Nonlinear diffusive equilibrium in three dimensions 5.6 Summary and References Problems Chapter 6. Compactness and Schauder's theorem 6.1 Continuous operators 6.2 Brouwer's theorem 6.3 Compactness 6.4 Relative compactness 6.5 Arzel's theorem 6.6 Schauder's theorems 6.7 Forced nonlinear oscillations 6.8 Swirling flow 6.9 Summary and References Problems Part III. Operators in Hilbert Space Chapter 7. Hilbert space 7.1 Inner product spaces 7.2 Orthogonal bases 7.3 Orthogonal expansions 7.4 The Bessel, Parseval, and Riesz-Fischer theorems 7.5 Orthogonal decomposition 7.6 Functionals on normed spaces 7.7 Functionals in Hilbert space 7.8 Weak convergence 7.9 Summary and References Problems Chapter 8. The Theory of operators 8.1 Bounded operators on normed spaces 8.2 The algebra of bounded operators 8.3 Self-adjoint operators 8.4 Eigenvalue problems for self-adjoint operators 8.5 Compact operators 8.6 Summary and References Problems Chapter 9. The Spectral theorem 9.1 The spectral theorem 9.2 Sturm-Liouville systems 9.3 Partial differential equations 9.4 The Fredholm alternative 9.5 Projection operators 9.6 Summary and References Problems Chapter 10. Variational methods 10.1 Positive operators 10.2 Approximation to the first eigenvalue 10.3 The Rayleigh-Ritz method for eigenvalues 10.4 The theory of the Rayleigh-Ritz method 10.5 Inhomogeneous Equations 10.6 Complementary bounds 10.7 Summary and References Problems Part IV. Further developments Chapter 11. The differential calculus of operators and its applications 11.1 The Frchet derivative 11.2 Higher derivatives 11.3 Maxima and Minima 11.4 Linear stability theory 11.5. Nonlinear stability 11.6 Bifurcation theory 11.7 Bifurcation and stability 11.8 Summary and References Chapter 12. Distributional Hilbert spaces 12.1 The space of square-integrable distributions 12.2 Sobolev spaces 12.3 Application to partial differential equations 12.4 Summary and References Appendix A. Sets and mappings Appendix B. Sequences, series, and uniform convergence Appendix C. Sup and inf Appendix D. Countability Appendix E. Equivalence relations Appendix F. Completion Appendix G. Sturm-Liouvil. Codice libro della libreria ABE_book_new_0486422585

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## 7.Applied Functional Analysis (Paperback)

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Descrizione libro Paperback. Condizione libro: New. 155mm x 20mm x 235mm. Paperback. This introductory text examines many important applications of functional analysis to mechanics, fluid mechanics, diffusive growth, and approximation. Discusses distribution theory, Green'.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 400 pages. 0.494. Codice libro della libreria 9780486422589

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