Verfügbarkeit: Inequalities :: THWS Bibkatalog

Inequalities:

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Bibliographische Detailangaben
Hauptverfasser:	Beckenbach, Edwin F. 1906-1982 (VerfasserIn), Bellman, Richard E. (VerfasserIn)
Format:	Buch
Sprache:	German
Veröffentlicht:	Berlin [u.a.] Springer 1971
Ausgabe:	3. print.
Schriftenreihe:	Ergebnisse der Mathematik und ihrer Grenzgebiete 30
Schlagworte:	Inequalities (Mathematics) Mathematical analysis Ungleichung
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XI, 198 S. Ill.
ISBN:	3540032835 0387032835

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Datensatz im Suchindex

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adam_text	Contents Chapter 1. The Fundamental Inequalities and Related Matters 1 § I. Introduction 1 § 2. The Cauchy Inequality 2 § 3. The Lagrange Identity 3 § 4. The Arithmetic mean — Geometric mean Inequality 3 § 5. Induction — Forward and Backward 4 § 6. Calculus and Lagrange Multipliers 5 § 7. Functional Equations 6 § 8. Concavity 6 § 9. Majorization — The Proof of Bohr 7 § 10. The Proof of Hurwitz 8 §11. A Proof of Ehlers 9 § 12. The Arithmetic geometric Mean of Gauss; the Elementary Symmetric Functions , 10 § 13. A Proof of Jacobsthal 11 § 14. A Fundamental Relationship 12 § 15. Young s Inequality 15 §16. The Means M, (, a) and the Sums S, () 16 § 17. The Inequalities of Holder and Minkowski 19 § 18. Extensions of the Classical Inequalities 20 § 19. Quasi Linearization 23 § 20. Minkowski s Inequality 25 §21. Another Inequality of Minkowski 26 § 22. Minkowski s Inequality for 0 p 1 26 § 23. An Inequality of Beckenbach 27 § 24. An Inequality of Dresher 28 § 25. Minkowski Mahler Inequality 28 § 26. Quasi Linearization of Convex and Concave Functions 29 § 27. Another Type of Quasi Linearization 30 § 28. An Inequality of Karamata 30 § 29. The Schur Transformation 31 § 30. Proof of the Karamata Result 31 §31. An Inequality of Ostrowski 32 § 32. Continuous Versions 32 § 33. Symmetric Functions 33 § 34. A Further Inequality 35 § 35. Some Results of Whiteley 35 § 36. Hyperbolic Polynomials 36 § 37. Garding s Inequality 37 §38. Examples 37 § 39. Lorentz Spaces 38 § 40. Converses of Inequalities 39 §41. i Case 41 § 42. Multidimensional Case 42 § 43. Generalizations of Favard Berwald 43 Contents IX § 44. Other Converses of the Cauchy Theorem 44 § 45. Refinements of the Cauchy Buniakowsky Schwarz Inequalities ... 45 § 46. A Result of Mohr and Noll 46 § 47. Generation of New Inequalities from Old 46 § 48. Refinement of Arithmetic mean — geometric mean Inequality ... 47 § 49. Inequalities with Alternating Signs 47 § 50. Steffensen s Inequality 48 §51. Brunk Olkin Inequality 49 § 52. Extensions of Steffensen s Inequality 49 Bibliographical Notes 50 Chapter 2. Positive Definite Matrices, Characteristic Roots, and Positive Matrices 55 § 1. Introduction 55 § 2. Positive Definite Matrices 57 § 3. A Necessary Condition for Positive Definiteness 57 § 4. Representation as a Sum of Squares 58 § 5. A Necessary and Sufficient Condition for Positive Definiteness ... 59 § 6. Gramians 59 § 7. Evaluation of an Infinite Integral 61 § 8. Complex Matrices with Positive Definite Real Part 62 § 9. A Concavity Theorem 62 § 10. An Inequality Concerning Minors 63 § 11. Hadamard s Inequality 64 § 12. Szasz s Inequality 64 § 13. A Representation Theorem for the Determinant of a Hermitian Matrix 65 § 14. Discussion 65 § 15. Ingham Siegel Integrals and Generalizations 65 § 16. Group Invariance and Representation Formulas 67 § 17. Bergstrom s Inequality 67 § 18. A Generalization 68 § 19. Canonical Form 68 § 20. A Generalization of Bergstrom s Inequality 69 §21. A Representation Theorem for \|^\| » 70 § 22. An Inequality of Minkowski 70 §23. A Generalization due to Ky Fan 71 § 24. A Generalization due to Oppenheim 71 §25. The Rayleigh Quotient 71 § 26. The Fischer Min max Theorem 72 § 27. A Representation Theorem 73 § 28. An Inequality of Ky Fan 74 § 29. An Additive Version 75 § 30. Results Connecting Characteristic Roots of A, A A, and (A + A)f2 75 §31. The Cauchy Poincar6 Separation Theorem 75 §32. An Inequality for A,At,_!... At 76 §33. Discussion 76 § 34. Additive Version 77 § 35. Multiplicative Inequality Derived from Additive 77 § 36. Further Results 78 § 37. Compound and Adjugate Matrices 79 § 38. Positive Matrices 80 §39. Variational Characterization of p{A) 81 § 40. A Modification due to Birkhoff and Varga 82 X Contents §41. Some Consequences 83 § 42. Input output Matrices 83 § 43. Discussion 84 § 44. Extensions 84 § 45. Matrices and Hyperbolic Equations 85 § 46. Nonvanishing of Determinants and the Location of Characteristic Values 85 § 47. Monotone Matrix Functions in the Sense of Loewner 86 § 48. Variation diminishing Transformations 86 § 49. Domains of Positivity 87 Bibliographical Notes 88 Chapter 3. Moment Spaces and Resonance Theorems 97 § 1. Introduction 97 § 2. Moments 102 § 3. Convexity 103 § 4. Some Examples of Convex Spaces 104 § 5. Examples of Nonconvex Spaces 105 § 6. On the Determination of Convex Sets 105 § 7. L Space — A Result of F. Riesz 106 § 8. Bounded Variation 108 § 9. Positivity 109 § 10. Representation as Squares 110 §11. Nonnegative Trigonometric and Rational Polynomials Ill § 12. Positive Definite Quadratic Forms and Moment Sequences 112 §13. Historical Note 112 § 14. Positive Definite Sequences 113 § 15. Positive Definite Functions 114 § 16. Reproducing Kernels 115 § 17. Nonconvex Spaces 115 § 18. A Resonance Theorem of Landau 116 §19. The Banach Steinhaus Theorem 118 § 20. A Theorem of Minkowski 118 §21. The Theory of Linear Inequalities 119 § 22. Generalizations 120 § 23. The Min max Theorem of von Neumann 120 § 24. The Neyman Pearson Lemma 121 § 25. Orthogonal Projection 123 §26. Equivalance of Minimization and Maximization Processes 124 Bibliographical Notes 125 Chapter 4. On the Positivity of Operators 131 § 1. Introduction 131 § 2. First order Linear Differential Equations 133 § 3. Discussion 134 § 4. A Fundamental Result in Stability Theory 134 § 5. Inequalities of Bihari Langenhop 135 § 6. Matrix Analogues 136 § 7. A Proof by Taussky 138 § 8. Variable Matrix 138 § 9. Discussion 139 § 10. A Result of Caplygin 139 § 11. Finite Intervals 140 Contents XI § 12. Variational Proof 141 § 13. Discussion 142 § 14. Linear Differential Equations of Arbitrary Order 142 § 15. A Positivity Result for Higher order Linear Differential Operators . .143 § 16. Some Results of P6lya 144 § 17. Generalized Convexity 145 § 18. Discussion 146 § 19. The Generalized Mean value Theorem of Hartman and Wintner . . 146 § 20. Generalized Taylor Expansions 147 §21. Positivity of Operators 147 § 22. Elliptic Equations 148 § 23. Positive Reproducing Kernels 149 § 24. Monotonicity of Mean Values 149 § 25. Positivity of the Parabolic Operator 150 §26. Finite difference Schemes 151 §27. Potential Equations 153 § 28. Discussion 153 §29. The Inequalities of Haar Westphal Prodi 154 § 30. Some Inequalities of Wendroff 154 § 31. Results of Weinberger Bochner 155 § 32. Variation diminishing Transformations 155 § 33. Quasi Linearization 155 § 34. Stability of Operators 156 § 35. Miscellaneous Results 157 Bibliographical Notes 157 Chapter 5. Inequalities for Differential Operators 164 § 1. Introduction 164 § 2. Some Inequalities of B. Sz. Naoy 166 § 3. Inequalities Connecting «, « , and u 168 § 4. Inequalities Connecting «, « * , and M( 170 § 5. Alternative Approach for «, « , and u 171 § 6. An Inequality of Halperin and von Neumann and Its Extensions . . 172 § 7. Results Analogous to Those of Nagy 175 § 8. Carlson s Inequality 175 § 9. Generalizations of Carlson s Inequality 175 § 10. Wirtinger s Inequality and Related Results 177 § 11. Proof Using Fourier Series 178 § 12. Sturm Liouville Theory 178 § 13. Integral Identities 179 § 14. Colautti s Results 180 § 15. Partial Differential Equations 180 § 16. Matrix Version 181 § 17. Higher Derivatives and Higher Powers 182 § 18. Discrete Versions of Fan, Taussky, and Todd 182* § 19. Discrete Case — Second Differences 183 § 20. Discrete Versions of Northcott Bellman Inequalities 183 §21. Discussion 184 Bibliographical Notes 185 Name Index 189 Subject Index 195
adam_txt	Contents Chapter 1. The Fundamental Inequalities and Related Matters 1 § I. Introduction 1 § 2. The Cauchy Inequality 2 § 3. The Lagrange Identity 3 § 4. The Arithmetic mean — Geometric mean Inequality 3 § 5. Induction — Forward and Backward 4 § 6. Calculus and Lagrange Multipliers 5 § 7. Functional Equations 6 § 8. Concavity 6 § 9. Majorization — The Proof of Bohr 7 § 10. The Proof of Hurwitz 8 §11. A Proof of Ehlers 9 § 12. The Arithmetic geometric Mean of Gauss; the Elementary Symmetric Functions , 10 § 13. A Proof of Jacobsthal 11 § 14. A Fundamental Relationship 12 § 15. Young's Inequality 15 §16. The Means M, (, a) and the Sums S, () 16 § 17. The Inequalities of Holder and Minkowski 19 § 18. Extensions of the Classical Inequalities 20 § 19. Quasi Linearization 23 § 20. Minkowski's Inequality 25 §21. Another Inequality of Minkowski 26 § 22. Minkowski's Inequality for 0 p 1 26 § 23. An Inequality of Beckenbach 27 § 24. An Inequality of Dresher 28 § 25. Minkowski Mahler Inequality 28 § 26. Quasi Linearization of Convex and Concave Functions 29 § 27. Another Type of Quasi Linearization 30 § 28. An Inequality of Karamata 30 § 29. The Schur Transformation 31 § 30. Proof of the Karamata Result 31 §31. An Inequality of Ostrowski 32 § 32. Continuous Versions 32 § 33. Symmetric Functions 33 § 34. A Further Inequality 35 § 35. Some Results of Whiteley 35 § 36. Hyperbolic Polynomials 36 § 37. Garding's Inequality 37 §38. Examples 37 § 39. Lorentz Spaces 38 § 40. Converses of Inequalities 39 §41. i'Case 41 § 42. Multidimensional Case 42 § 43. Generalizations of Favard Berwald 43 Contents IX § 44. Other Converses of the Cauchy Theorem 44 § 45. Refinements of the Cauchy Buniakowsky Schwarz Inequalities . 45 § 46. A Result of Mohr and Noll 46 § 47. Generation of New Inequalities from Old 46 § 48. Refinement of Arithmetic mean — geometric mean Inequality . 47 § 49. Inequalities with Alternating Signs 47 § 50. Steffensen's Inequality 48 §51. Brunk Olkin Inequality 49 § 52. Extensions of Steffensen's Inequality 49 Bibliographical Notes 50 Chapter 2. Positive Definite Matrices, Characteristic Roots, and Positive Matrices 55 § 1. Introduction 55 § 2. Positive Definite Matrices 57 § 3. A Necessary Condition for Positive Definiteness 57 § 4. Representation as a Sum of Squares 58 § 5. A Necessary and Sufficient Condition for Positive Definiteness . 59 § 6. Gramians 59 § 7. Evaluation of an Infinite Integral 61 § 8. Complex Matrices with Positive Definite Real Part 62 § 9. A Concavity Theorem 62 § 10. An Inequality Concerning Minors 63 § 11. Hadamard's Inequality 64 § 12. Szasz's Inequality 64 § 13. A Representation Theorem for the Determinant of a Hermitian Matrix 65 § 14. Discussion 65 § 15. Ingham Siegel Integrals and Generalizations 65 § 16. Group Invariance and Representation Formulas 67 § 17. Bergstrom's Inequality 67 § 18. A Generalization 68 § 19. Canonical Form 68 § 20. A Generalization of Bergstrom's Inequality 69 §21. A Representation Theorem for \|^\|"» 70 § 22. An Inequality of Minkowski 70 §23. A Generalization due to Ky Fan 71 § 24. A Generalization due to Oppenheim 71 §25. The Rayleigh Quotient 71 § 26. The Fischer Min max Theorem 72 § 27. A Representation Theorem 73 § 28. An Inequality of Ky Fan 74 § 29. An Additive Version 75 § 30. Results Connecting Characteristic Roots of A, A A, and (A + A)f2 75 §31. The Cauchy Poincar6 Separation Theorem 75 §32. An Inequality for A,At,_!. At 76 §33. Discussion 76 § 34. Additive Version 77 § 35. Multiplicative Inequality Derived from Additive 77 § 36. Further Results 78 § 37. Compound and Adjugate Matrices 79 § 38. Positive Matrices 80 §39. Variational Characterization of p{A) 81 § 40. A Modification due to Birkhoff and Varga 82 X Contents §41. Some Consequences 83 § 42. Input output Matrices 83 § 43. Discussion 84 § 44. Extensions 84 § 45. Matrices and Hyperbolic Equations 85 § 46. Nonvanishing of Determinants and the Location of Characteristic Values 85 § 47. Monotone Matrix Functions in the Sense of Loewner 86 § 48. Variation diminishing Transformations 86 § 49. Domains of Positivity 87 Bibliographical Notes 88 Chapter 3. Moment Spaces and Resonance Theorems 97 § 1. Introduction 97 § 2. Moments 102 § 3. Convexity 103 § 4. Some Examples of Convex Spaces 104 § 5. Examples of Nonconvex Spaces 105 § 6. On the Determination of Convex Sets 105 § 7. L" Space — A Result of F. Riesz 106 § 8. Bounded Variation 108 § 9. Positivity 109 § 10. Representation as Squares 110 §11. Nonnegative Trigonometric and Rational Polynomials Ill § 12. Positive Definite Quadratic Forms and Moment Sequences 112 §13. Historical Note 112 § 14. Positive Definite Sequences 113 § 15. Positive Definite Functions 114 § 16. Reproducing Kernels 115 § 17. Nonconvex Spaces 115 § 18. A "Resonance" Theorem of Landau 116 §19. The Banach Steinhaus Theorem 118 § 20. A Theorem of Minkowski 118 §21. The Theory of Linear Inequalities 119 § 22. Generalizations 120 § 23. The Min max Theorem of von Neumann 120 § 24. The Neyman Pearson Lemma 121 § 25. Orthogonal Projection 123 §26. Equivalance of Minimization and Maximization Processes 124 Bibliographical Notes 125 Chapter 4. On the Positivity of Operators 131 § 1. Introduction 131 § 2. First order Linear Differential Equations 133 § 3. Discussion 134 § 4. A Fundamental Result in Stability Theory 134 § 5. Inequalities of Bihari Langenhop 135 § 6. Matrix Analogues 136 § 7. A Proof by Taussky 138 § 8. Variable Matrix 138 § 9. Discussion 139 § 10. A Result of Caplygin 139 § 11. Finite Intervals 140 Contents XI § 12. Variational Proof 141 § 13. Discussion 142 § 14. Linear Differential Equations of Arbitrary Order 142 § 15. A Positivity Result for Higher order Linear Differential Operators . .143 § 16. Some Results of P6lya 144 § 17. Generalized Convexity 145 § 18. Discussion 146 § 19. The Generalized Mean value Theorem of Hartman and Wintner . . 146 § 20. Generalized Taylor Expansions 147 §21. Positivity of Operators 147 § 22. Elliptic Equations 148 § 23. Positive Reproducing Kernels 149 § 24. Monotonicity of Mean Values 149 § 25. Positivity of the Parabolic Operator 150 §26. Finite difference Schemes 151 §27. Potential Equations 153 § 28. Discussion 153 §29. The Inequalities of Haar Westphal Prodi 154 § 30. Some Inequalities of Wendroff 154 § 31. Results of Weinberger Bochner 155 § 32. Variation diminishing Transformations 155 § 33. Quasi Linearization 155 § 34. Stability of Operators 156 § 35. Miscellaneous Results 157 Bibliographical Notes 157 Chapter 5. Inequalities for Differential Operators 164 § 1. Introduction 164 § 2. Some Inequalities of B. Sz. Naoy 166 § 3. Inequalities Connecting «, «', and u" 168 § 4. Inequalities Connecting «, « * , and M("' 170 § 5. Alternative Approach for «, «', and u" 171 § 6. An Inequality of Halperin and von Neumann and Its Extensions . . 172 § 7. Results Analogous to Those of Nagy 175 § 8. Carlson's Inequality 175 § 9. Generalizations of Carlson's Inequality 175 § 10. Wirtinger's Inequality and Related Results 177 § 11. Proof Using Fourier Series 178 § 12. Sturm Liouville Theory 178 § 13. Integral Identities 179 § 14. Colautti's Results 180 § 15. Partial Differential Equations 180 § 16. Matrix Version 181 § 17. Higher Derivatives and Higher Powers 182 § 18. Discrete Versions of Fan, Taussky, and Todd 182* § 19. Discrete Case — Second Differences 183 § 20. Discrete Versions of Northcott Bellman Inequalities 183 §21. Discussion 184 Bibliographical Notes 185 Name Index 189 Subject Index 195
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spelling	Beckenbach, Edwin F. 1906-1982 Verfasser (DE-588)1066772495 aut Inequalities E. F. Beckenbach ; R. Bellman 3. print. Berlin [u.a.] Springer 1971 XI, 198 S. Ill. txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 30 Inequalities (Mathematics) Mathematical analysis Ungleichung (DE-588)4139098-2 gnd rswk-swf Ungleichung (DE-588)4139098-2 s DE-604 Bellman, Richard E. Verfasser aut Ergebnisse der Mathematik und ihrer Grenzgebiete 30 (DE-604)BV005871160 30 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015332040&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Beckenbach, Edwin F. 1906-1982 Bellman, Richard E. Inequalities Ergebnisse der Mathematik und ihrer Grenzgebiete Inequalities (Mathematics) Mathematical analysis Ungleichung (DE-588)4139098-2 gnd
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title	Inequalities
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title_exact_search	Inequalities
title_exact_search_txtP	Inequalities
title_full	Inequalities E. F. Beckenbach ; R. Bellman
title_fullStr	Inequalities E. F. Beckenbach ; R. Bellman
title_full_unstemmed	Inequalities E. F. Beckenbach ; R. Bellman
title_short	Inequalities
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topic	Inequalities (Mathematics) Mathematical analysis Ungleichung (DE-588)4139098-2 gnd
topic_facet	Inequalities (Mathematics) Mathematical analysis Ungleichung
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