# Linear Operator Theory in Engineering and Science

## Naylor, Arch W.; Sell, George R.

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A unique introduction to the theory of linear operators on Hilbert space. The author presents the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented.

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Recensione:

A.W. Naylor and G.R. Sell

Linear Operator Theory in Engineering and Science

"Vivid and easily understandable . . . numerous exercises . . . have greatly advanced the understanding of material presented in the book . . . can be used by students with various level of preparation with different interests, as well as a textbook for a senior-level courses."—ZENTRALBLATT MATH

Contenuti:

1 Introduction.- 1. Black Boxes.- 2. Structure of the Plane.- 3. Mathematical Modeling.- 4. The Axiomatic Method. The Process of Abstraction.- 5. Proofs of Theorems.- 2 Set-Theoretic Structure.- 1. Introduction.- 2. Basic Set Operations.- 3. Cartesian Products.- 4. Sets of Numbers.- 5. Equivalence Relations and Partitions.- 6. Functions.- 7. Inverses.- 8. Systems Types.- 3 Topological Structure.- 1. Introduction.- A Introduction to Metric Spaces.- 2. Metric Spaces: Definition.- 3. Examples of Metric Spaces.- 4. Subspaces and Product Spaces.- 5. Continuous Functions.- 6. Convergent Sequences.- 7. A Connection Between Continuity and Convergence.- B Some Deeper Metric Space Concepts.- 8. Local Neighborhoods.- 9. Open Sets.- 10. More on Open Sets.- 11. Examples of Homeomorphic Metric Spaces.- 12. Closed Sets and the Closure Operation.- 13. Completeness.- 14. Completion of Metric Spaces.- 15. Contraction Mapping.- 16. Total Boundedness and Approximations.- 17. Compactness.- 4 Algebraic Structure.- 1. Introduction.- A Introduction to Linear Spaces.- 2. Linear Spaces and Linear Subspaces.- 3. Linear Transformations.- 4. Inverse Transformations.- 5. Isomorphisms.- 6. Linear Independence and Dependence.- 7. Hamel Bases and Dimension.- 8. The Use of Matrices to Represent Linear Transformations.- 9. Equivalent Linear Transformations.- B Further Topics.- 10. Direct Sums and Sums.- 11. Projections.- 12. Linear Functionals and the Algebraic Conjugate of a Linear Space.- 13. Transpose of a Linear Transformation.- 5 Combined Topological and Algebraic Structure.- 1. Introduction.- A Banach Spaces.- 2. Definitions.- 3. Examples of Normal Linear Spaces.- 4. Sequences and Series.- 5. Linear Subspaces.- 6. Continuous Linear Transformations.- 7. Inverses and Continuous Inverses.- 8. Operator Topologies.- 9. Equivalence of Normed Linear Spaces.- 10. Finite-Dimensional Spaces.- 11. Normed Conjugate Space and Conjugate Operator.- B Hilbert Spaces.- 12. Inner Product and Hilbert Spaces.- 13. Examples.- 14. Orthogonality.- 15. Orthogonal Complements and the Projection Theorem.- 16. Orthogonal Projections.- 17. Orthogonal Sets and Bases: Generalized Fourier Series.- 18. Examples of Orthonormal Bases.- 19. Unitary Operators and Equivalent Inner Product Spaces.- 20. Sums and Direct Sums of Hilbert Spaces.- 21. Continuous Linear Functionals.- C Special Operators.- 22. The Adjoint Operator.- 23. Normal and Self-Adjoint Operators.- 24. Compact Operators.- 25. Foundations of Quantum Mechanics.- 6 Analysis of Linear Operators (Compact Case).- 1. Introduction.- A An Illustrative Example.- 2. Geometric Analysis of Operators.- 3. Geometric Analysis. The Eigenvalue-Eigenvector Problem.- >4. A Finite-Dimensional Problem.- B The Spectrum.- 5. The Spectrum of Linear Transformations.- 6. Examples of Spectra.- 7. Properties of the Spectrum.- C Spectral Analysis.- 8. Resolutions of the Identity.- 9. Weighted Sums of Projections.- 10. Spectral Properties of Compact, Normal, and Self-Adjoint Operators.- 11. The Spectral Theorem.- 12. Functions of Operators (Operational Calculus).- 13. Applications of the Spectral Theorem.- 14. Nonnormal Operators.- 7 Analysis of Unbounded Operators.- 1. Introduction.- 2. Green’s Functions.- 3. Symmetric Operators.- 4. Examples of Symmetric Operators.- 5. Sturm-Liouville Operators.- 6. Gårding’s Inequality.- 7. Elliptic Partial Differential Operators.- 8. The Dirichlet Problem.- 9. The Heat Equation and Wave Equation.- 10. Self-Adjoint Operators.- 11. The Cayley Transform.- 12. Quantum Mechanics, Revisited.- 13. Heisenberg Uncertainty Principle.- 14. The Harmonic Oscillator.- Appendix A The Hölder, Schwartz, and Minkowski Inequalities.- Appendix B Cardinality.- Appendix C Zorn’s Lemma.- Appendix D Integration and Measure Theory.- 1. Introduction.- 2. The Riemann Integral.- 3. A Problem with the Riemann Integral.- 5. Null Sets.- 6. Convergence Almost Everywhere.- 7. The Lebesgue Integral.- 8. Limit Theorems.- 9. Miscellany.- 10. Other Definitions of the Integral.- 13. Differentiation.- 14. The Radon-Nikodym Theorem.- 15. Fubini Theorem.- Appendix E Probability Spaces and Stochastic Processes.- 1. Probability Spaces.- 2. Random Variables and Probability Distributions.- 3. Expectation.- 4. Stochastic Independence.- 5. Conditional Expectation Operator.- 6. Stochastic Processes.- Index of Symbols.

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## 1.Linear Operator Theory in Engineering and Science

Editore: Springer 2000-03 (2000)
ISBN 10: 038795001X ISBN 13: 9780387950013
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Descrizione libro Springer 2000-03, 2000. Condizione libro: New. This item is printed on demand. Brand new book, sourced directly from publisher. Dispatch time is 24-48 hours from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Codice libro della libreria NU-LSI-06926941

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## 2.Linear Operator Theory in Engineering and Science (Paperback)

Editore: Springer-Verlag New York Inc., United States (2000)
ISBN 10: 038795001X ISBN 13: 9780387950013
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Descrizione libro Springer-Verlag New York Inc., United States, 2000. Paperback. Condizione libro: New. 1st ed. 1982. 2nd printing 2000. 231 x 155 mm. Language: English . Brand New Book ***** Print on Demand *****. A unique introduction to the theory of linear operators on Hilbert space. The author presents the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented. Codice libro della libreria AAV9780387950013

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## 3.Linear Operator Theory in Engineering and Science (Paperback)

Editore: Springer-Verlag New York Inc., United States (2000)
ISBN 10: 038795001X ISBN 13: 9780387950013
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Descrizione libro Springer-Verlag New York Inc., United States, 2000. Paperback. Condizione libro: New. 1st ed. 1982. 2nd printing 2000. 231 x 155 mm. Language: English . Brand New Book ***** Print on Demand *****.A unique introduction to the theory of linear operators on Hilbert space. The author presents the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented. Codice libro della libreria AAV9780387950013

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## 4.Linear Operator Theory in Engineering and Science

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Descrizione libro Springer Verlag, 2000. Paperback. Condizione libro: Brand New. reprint edition. 624 pages. 9.00x6.25x1.25 inches. In Stock. Codice libro della libreria __038795001X

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## 5.Linear Operator Theory in Engineering and Science

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Descrizione libro Springer-Verlag New York Inc., 2000. PAP. Condizione libro: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria LQ-9780387950013

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## 6.Linear Operator Theory in Engineering and Science

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Descrizione libro Springer, 2000. Paperback. Condizione libro: NEW. 9780387950013 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0411235

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## 7.Linear Operator Theory in Engineering and Science

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Descrizione libro Springer-Verlag New York Inc., 2000. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria I2-9780387950013

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## 8.Linear Operator Theory in Engineering and Science

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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 ria9780387950013_lsuk

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## 9.Linear Operator Theory in Engineering and Science (Applied Mathematical Sciences)

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Descrizione libro Springer, 2000. Paperback. Condizione libro: New. book. Codice libro della libreria 038795001X

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## 10.Linear Operator Theory in Engineering and Science (Applied Mathematical Sciences)

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Descrizione libro Springer, 2000. Paperback. Condizione libro: New. This item is printed on demand. Codice libro della libreria DADAX038795001X

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