The Resource Regular variation, N.H. Bingham, C.M. Goldie, J.L. Teugels, (electronic resource)

Regular variation, N.H. Bingham, C.M. Goldie, J.L. Teugels, (electronic resource)

Label
Regular variation
Title
Regular variation
Statement of responsibility
N.H. Bingham, C.M. Goldie, J.L. Teugels
Creator
Contributor
Subject
Genre
Language
  • eng
  • eng
Summary
A comprehensive account of the theory and applications of regular variation
Member of
Cataloging source
MiAaPQ
http://library.link/vocab/creatorName
Bingham, N. H
Dewey number
515.8
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA331.5
LC item number
.B54 1987
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • Goldie, C. M
  • Teugels, Jef L
Series statement
  • Encyclopedia of mathematics and its applications
  • Encyclopedia of Mathematics and its Applications
Series volume
v. 27
http://library.link/vocab/subjectName
  • Functions of real variables
  • Calculus
Label
Regular variation, N.H. Bingham, C.M. Goldie, J.L. Teugels, (electronic resource)
Instantiates
Publication
Note
Includes indexes
Bibliography note
Bibliography: p. [445]-466
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Cover; Half Title; Title; Copyright; Dedication; CONTENTS; PREFACE; 1 Karamata Theory; 1.0 Introduction; 1.1 Steinhaus Theory and additive functions; 1. Additive functions; 2. Steinhaus Theory; 3. The Cauchy functional equation; 4. Pathological solutions; 5. Multiplicative notation; 1.2 The Uniform Convergence Theorem; 1. The Theorem; 2. Direct proofs; 3. Indirect proofs; 4. Pathology; 5. Remarks; 1.3 The Representation Theorem; 1. The Theorem; 2. Variants; 3. Examples and properties; 1.4 The Characterisation Theorem; 1.The limit functions; 2. Regular variation
  • 3. Other characterisation theorems4. Weak regular variation; 5. Discussion; 1.5 Functions of regular variation; 1. Uniform convergence and representation; 2. Monotone equivalents; 3. The Zygmund class; 4. Potter bounds; 5. Properties; 6. Karamata's Theorem (direct half); 7. Asymptotic inversion and conjugacy; 1.6 Karamata's Theorem; 1. Converse half; 2. The Aljancic-Karamata Theorem; 3. Stieltjes-integral forms; 4. Frullani integrals; 1.7 Tauberian Theorems; 1. LS transforms; 2. Karamata's Tauberian Theorem; 3. Monotone Density Theorem; 4. Power series; 5. Stieltjes transforms
  • 6. Slow decrease1.8 Smooth variation; 1. The Smooth Variation Theorem; 2. Properties; 3. The group SR+; 4. de Bruijn and Young conjugates; 1.9 Sequences; 1.10 Monotonicity; 1.11 Exercises and complements; 2 Further Karamata Theory; 2.0 Extensions: R c ER cOR; 1. Uniformity theorems; 2. Extensions of regular variation; 2.1 Karamata and Matuszewska indices; 1. Karamata indices; 2. Matuszewska indices; 2.2. Further properties of ER and OR; 1. Almost increasing and almost decreasing functions; 2. Orders; 3. Representations; 2.3 Rates of convergence and growth; 1. Rates of slow variation
  • 2. de Bruijn conjugates3. Rates of growth; 4. Approximation by a regularly varying function; 2.4 Rapid variation; 1. Function classes; 2. Uniform Convergence Theorem; 3. Characterisations and representations; 4. Maximum and inverse; 2.5 Pólya peaks; 2.6 'Karamata's Theorem' for one-sided indices; 1. Ratio of function and integral; 2. Stieltjes versions; 3. Rapid variation; 2.7 Quasi- and near-mono tonicity; 1. Definitions; 2. Representations; 3. Examples; 2.8 Gauge-functions; 2.9 Exceptional sets; 2.10 Tauberian Theorems; 1. Ratio Tauberian Theorem
  • 2. A Tauberian theorem for dominated variation3. O-version of Monotone Density Theorem; 2.11 Beurling slow variation and its relatives; 2.12 Exercises and complements; 3 de Haan Theory; 3.0 Introduction, definitions, notation; 3.1 Uniformity; 1. Upper bounds; 2. Bounds; 3. Both sides of 1; 4. Function classes; 5. Bounded decrease of auxiliary function; 6. Positive increase and decrease of auxiliary function; 7. Specified right-hand side; 6. Rapid variation; 3.2 Limits; 1. Limits under measurability; 2. Limits without measurability of f; 3.3 Local indices and EIlg; 3.4 Global indices and OIlg
  • 3.5 The indices transform
Dimensions
unknown
Extent
1 online resource (518 p.)
Form of item
online
Isbn
9781107099890
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2670000000393841
  • (EBL)1178980
  • (OCoLC)853359881
  • (SSID)ssj0000918580
  • (PQKBManifestationID)12467265
  • (PQKBTitleCode)TC0000918580
  • (PQKBWorkID)10907786
  • (PQKB)10852180
  • (UkCbUP)CR9780511721434
  • (MiAaPQ)EBC1178980
  • (EXLCZ)992670000000393841
Label
Regular variation, N.H. Bingham, C.M. Goldie, J.L. Teugels, (electronic resource)
Publication
Note
Includes indexes
Bibliography note
Bibliography: p. [445]-466
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Cover; Half Title; Title; Copyright; Dedication; CONTENTS; PREFACE; 1 Karamata Theory; 1.0 Introduction; 1.1 Steinhaus Theory and additive functions; 1. Additive functions; 2. Steinhaus Theory; 3. The Cauchy functional equation; 4. Pathological solutions; 5. Multiplicative notation; 1.2 The Uniform Convergence Theorem; 1. The Theorem; 2. Direct proofs; 3. Indirect proofs; 4. Pathology; 5. Remarks; 1.3 The Representation Theorem; 1. The Theorem; 2. Variants; 3. Examples and properties; 1.4 The Characterisation Theorem; 1.The limit functions; 2. Regular variation
  • 3. Other characterisation theorems4. Weak regular variation; 5. Discussion; 1.5 Functions of regular variation; 1. Uniform convergence and representation; 2. Monotone equivalents; 3. The Zygmund class; 4. Potter bounds; 5. Properties; 6. Karamata's Theorem (direct half); 7. Asymptotic inversion and conjugacy; 1.6 Karamata's Theorem; 1. Converse half; 2. The Aljancic-Karamata Theorem; 3. Stieltjes-integral forms; 4. Frullani integrals; 1.7 Tauberian Theorems; 1. LS transforms; 2. Karamata's Tauberian Theorem; 3. Monotone Density Theorem; 4. Power series; 5. Stieltjes transforms
  • 6. Slow decrease1.8 Smooth variation; 1. The Smooth Variation Theorem; 2. Properties; 3. The group SR+; 4. de Bruijn and Young conjugates; 1.9 Sequences; 1.10 Monotonicity; 1.11 Exercises and complements; 2 Further Karamata Theory; 2.0 Extensions: R c ER cOR; 1. Uniformity theorems; 2. Extensions of regular variation; 2.1 Karamata and Matuszewska indices; 1. Karamata indices; 2. Matuszewska indices; 2.2. Further properties of ER and OR; 1. Almost increasing and almost decreasing functions; 2. Orders; 3. Representations; 2.3 Rates of convergence and growth; 1. Rates of slow variation
  • 2. de Bruijn conjugates3. Rates of growth; 4. Approximation by a regularly varying function; 2.4 Rapid variation; 1. Function classes; 2. Uniform Convergence Theorem; 3. Characterisations and representations; 4. Maximum and inverse; 2.5 Pólya peaks; 2.6 'Karamata's Theorem' for one-sided indices; 1. Ratio of function and integral; 2. Stieltjes versions; 3. Rapid variation; 2.7 Quasi- and near-mono tonicity; 1. Definitions; 2. Representations; 3. Examples; 2.8 Gauge-functions; 2.9 Exceptional sets; 2.10 Tauberian Theorems; 1. Ratio Tauberian Theorem
  • 2. A Tauberian theorem for dominated variation3. O-version of Monotone Density Theorem; 2.11 Beurling slow variation and its relatives; 2.12 Exercises and complements; 3 de Haan Theory; 3.0 Introduction, definitions, notation; 3.1 Uniformity; 1. Upper bounds; 2. Bounds; 3. Both sides of 1; 4. Function classes; 5. Bounded decrease of auxiliary function; 6. Positive increase and decrease of auxiliary function; 7. Specified right-hand side; 6. Rapid variation; 3.2 Limits; 1. Limits under measurability; 2. Limits without measurability of f; 3.3 Local indices and EIlg; 3.4 Global indices and OIlg
  • 3.5 The indices transform
Dimensions
unknown
Extent
1 online resource (518 p.)
Form of item
online
Isbn
9781107099890
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2670000000393841
  • (EBL)1178980
  • (OCoLC)853359881
  • (SSID)ssj0000918580
  • (PQKBManifestationID)12467265
  • (PQKBTitleCode)TC0000918580
  • (PQKBWorkID)10907786
  • (PQKB)10852180
  • (UkCbUP)CR9780511721434
  • (MiAaPQ)EBC1178980
  • (EXLCZ)992670000000393841

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