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The Resource A Distributional Approach to Asymptotics : Theory and Applications, by Ricardo Estrada, Ram P. Kanwal, (electronic resource)
A Distributional Approach to Asymptotics : Theory and Applications, by Ricardo Estrada, Ram P. Kanwal, (electronic resource)
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The item A Distributional Approach to Asymptotics : Theory and Applications, by Ricardo Estrada, Ram P. Kanwal, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item A Distributional Approach to Asymptotics : Theory and Applications, by Ricardo Estrada, Ram P. Kanwal, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 " ... The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book ... [it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is.""The Bulletin of Mathematics Books" (Review of the 1st edition) ** " ... The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field ... most of the material has appeared in no other book.""SIAM News" (Review of the 1st edition) This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory. Key features of this significantly expanded and revised second edition: * addition of a new chapter and many new sections * wide range of topics covered, including the Ces.ro behavior of distributions and their connections to asymptotic analysis, the study of timedomain asymptotics, and the use of series of Dirac delta functions to solve boundary value problems * novel approach detailing the interplay between underlying theories of asymptotic analysis and generalized functions * extensive examples and exercises at the end of each chapter * comprehensive bibliography and index This work is an excellent tool for the classroom and an invaluable selfstudy resource that will stimulate application of asymptotic
 Language
 eng
 Edition
 Second edition.
 Extent
 1 online resource (xv, 451 pages 3 illustrations).
 Contents

 1 Basic Results in Asymptotics
 1.1 Introduction
 1.2 Order Symbols
 1.3 Asymptotic Series
 1.4 Algebraic and Analytic Operations
 1.5 Existence of Functions with a Given Asymptotic Expansion
 1.6 Asymptotic Power Series in a Complex Variable
 1.7 Asymptotic Approximation of Partial Sums
 1.8 The EulerMaclaurin Summation Formula
 1.9 Exercises
 2 Introduction to the Theory of Distributions
 2.1 Introduction
 2.2 The Space of Distributions D?
 2.3 Algebraic and Analytic Operations
 2.4 Regularization, Pseudofunction and Hadamard Finite Part
 2.5 Support and Order
 2.6 Homogeneous Distributions
 2.7 Distributional Derivatives of Discontinuous Functions
 2.8 Tempered Distributions and the Fourier Transform
 2.9 Distributions of Rapid Decay
 2.10 Spaces of Distributions Associated with an Asymptotic Sequence
 2.11 Exercises
 3 A Distributional Theory for Asymptotic Expansions
 3.1 Introduction
 3.2 The Taylor Expansion of Distributions
 3.3 The Moment Asymptotic Expansion
 3.4 Expansions in the Space P?
 3.5 Laplace's Asymptotic Formula
 3.6 The Method of Steepest Descent
 3.7 Expansion of Oscillatory Kernels
 3.8 TimeDomain Asymptotics
 3.9 The Expansion of f (?x) as ? ? ? in Other Cases
 3.10 Asymptotic Separation of Variables
 3.11 Exercises
 4 Asymptotic Expansion of Multidimensional Generalized Functions
 4.1 Introduction
 4.2 Taylor Expansion in Several Variables
 4.3 The Multidimensional Moment Asymptotic Expansion
 4.4 Laplace's Asymptotic Formula
 4.5 Fourier Type Integrals
 4.6 TimeDomain Asymptotics
 4.7 Further Examples
 4.8 Tensor Products and Partial Asymptotic Expansions
 4.9 An Application in Quantum Mechanics
 4.10 Expansion of Kernels of the Type f (?x, x)
 4.11 Exercises
 5 Asymptotic Expansion of Certain Series Considered by Ramanujan
 5.1 Introduction
 5.2 Basic Formulas
 5.3 Lambert Type Series
 5.4 Distributionally Small Sequences
 5.5 Multiple Series
 5.6 Unrestricted Partitions
 5.7 Exercises
 6 Cesàro Behavior of Distributions
 6.1 Introduction
 6.2 Summability of Series and Integrals
 6.3 The Behavior of Distributions in the (C) Sense
 6.4 The Cesàro Summability of Evaluations
 6.5 Parametric Behavior
 6.6 Characterization of Tempered Distributions
 6.7 The Space K?
 6.8 Spherical Means
 6.9 Existence of Regularizations
 6.10 The Integral Test
 6.11 Moment Functions
 6.12 The Analytic Continuation of Zeta Functions
 6.13 Fourier Series
 6.14 Summability of Trigonometric Series
 6.15 Distributional Point Values of Fourier Series
 6.16 Spectral Asymptotics
 6.17 Pointwise and Average Expansions
 6.18 Global Expansions
 6.19 Asymptotics of the Coincidence Limit
 6.20 Exercises
 7 Series of Dirac Delta Functions
 7.1 Introduction
 7.2 Basic Notions
 7.3 Several Problems that Lead to Series of Deltas
 7.4 Dual Taylor Series as Asymptotics of Solutions of Equations
 7.5 Boundary Layers
 7.6 Spectral Content Asymptotics
 7.7 Exercises
 References
 Isbn
 9780817681302
 Label
 A Distributional Approach to Asymptotics : Theory and Applications
 Title
 A Distributional Approach to Asymptotics
 Title remainder
 Theory and Applications
 Statement of responsibility
 by Ricardo Estrada, Ram P. Kanwal
 Language
 eng
 Summary
 " ... The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book ... [it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is.""The Bulletin of Mathematics Books" (Review of the 1st edition) ** " ... The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field ... most of the material has appeared in no other book.""SIAM News" (Review of the 1st edition) This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory. Key features of this significantly expanded and revised second edition: * addition of a new chapter and many new sections * wide range of topics covered, including the Ces.ro behavior of distributions and their connections to asymptotic analysis, the study of timedomain asymptotics, and the use of series of Dirac delta functions to solve boundary value problems * novel approach detailing the interplay between underlying theories of asymptotic analysis and generalized functions * extensive examples and exercises at the end of each chapter * comprehensive bibliography and index This work is an excellent tool for the classroom and an invaluable selfstudy resource that will stimulate application of asymptotic
 Cataloging source
 AU@
 http://library.link/vocab/creatorName
 Estrada, Ricardo
 Dewey number
 515
 Illustrations
 illustrations
 Index
 no index present
 LC call number
 QA299.6433
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 Kanwal, Ram P
 Series statement
 Birkhäuser Advanced Texts, Basler Lehrbücher
 http://library.link/vocab/subjectName

 Mathematics
 Global analysis (Mathematics)
 Mathematical statistics
 Global analysis (Mathematics)
 Mathematical statistics
 Mathematics
 Label
 A Distributional Approach to Asymptotics : Theory and Applications, by Ricardo Estrada, Ram P. Kanwal, (electronic resource)
 Antecedent source
 file reproduced from original
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 mixed
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 1 Basic Results in Asymptotics  1.1 Introduction  1.2 Order Symbols  1.3 Asymptotic Series  1.4 Algebraic and Analytic Operations  1.5 Existence of Functions with a Given Asymptotic Expansion  1.6 Asymptotic Power Series in a Complex Variable  1.7 Asymptotic Approximation of Partial Sums  1.8 The EulerMaclaurin Summation Formula  1.9 Exercises  2 Introduction to the Theory of Distributions  2.1 Introduction  2.2 The Space of Distributions D?  2.3 Algebraic and Analytic Operations  2.4 Regularization, Pseudofunction and Hadamard Finite Part  2.5 Support and Order  2.6 Homogeneous Distributions  2.7 Distributional Derivatives of Discontinuous Functions  2.8 Tempered Distributions and the Fourier Transform  2.9 Distributions of Rapid Decay  2.10 Spaces of Distributions Associated with an Asymptotic Sequence  2.11 Exercises  3 A Distributional Theory for Asymptotic Expansions  3.1 Introduction  3.2 The Taylor Expansion of Distributions  3.3 The Moment Asymptotic Expansion  3.4 Expansions in the Space P?  3.5 Laplace's Asymptotic Formula  3.6 The Method of Steepest Descent  3.7 Expansion of Oscillatory Kernels  3.8 TimeDomain Asymptotics  3.9 The Expansion of f (?x) as ? ? ? in Other Cases  3.10 Asymptotic Separation of Variables  3.11 Exercises  4 Asymptotic Expansion of Multidimensional Generalized Functions  4.1 Introduction  4.2 Taylor Expansion in Several Variables  4.3 The Multidimensional Moment Asymptotic Expansion  4.4 Laplace's Asymptotic Formula  4.5 Fourier Type Integrals  4.6 TimeDomain Asymptotics  4.7 Further Examples  4.8 Tensor Products and Partial Asymptotic Expansions  4.9 An Application in Quantum Mechanics  4.10 Expansion of Kernels of the Type f (?x, x)  4.11 Exercises  5 Asymptotic Expansion of Certain Series Considered by Ramanujan  5.1 Introduction  5.2 Basic Formulas  5.3 Lambert Type Series  5.4 Distributionally Small Sequences  5.5 Multiple Series  5.6 Unrestricted Partitions  5.7 Exercises  6 Cesàro Behavior of Distributions  6.1 Introduction  6.2 Summability of Series and Integrals  6.3 The Behavior of Distributions in the (C) Sense  6.4 The Cesàro Summability of Evaluations  6.5 Parametric Behavior  6.6 Characterization of Tempered Distributions  6.7 The Space K?  6.8 Spherical Means  6.9 Existence of Regularizations  6.10 The Integral Test  6.11 Moment Functions  6.12 The Analytic Continuation of Zeta Functions  6.13 Fourier Series  6.14 Summability of Trigonometric Series  6.15 Distributional Point Values of Fourier Series  6.16 Spectral Asymptotics  6.17 Pointwise and Average Expansions  6.18 Global Expansions  6.19 Asymptotics of the Coincidence Limit  6.20 Exercises  7 Series of Dirac Delta Functions  7.1 Introduction  7.2 Basic Notions  7.3 Several Problems that Lead to Series of Deltas  7.4 Dual Taylor Series as Asymptotics of Solutions of Equations  7.5 Boundary Layers  7.6 Spectral Content Asymptotics  7.7 Exercises  References
 Dimensions
 unknown
 Edition
 Second edition.
 Extent
 1 online resource (xv, 451 pages 3 illustrations).
 File format
 unknown
 Form of item
 online
 Isbn
 9780817681302
 Isbn Type
 (electronic bk.)
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9780817681302
 Quality assurance targets
 unknown
 Reformatting quality
 access
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)853261332
 (OCoLC)ocn853261332
 Label
 A Distributional Approach to Asymptotics : Theory and Applications, by Ricardo Estrada, Ram P. Kanwal, (electronic resource)
 Antecedent source
 file reproduced from original
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 mixed
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 1 Basic Results in Asymptotics  1.1 Introduction  1.2 Order Symbols  1.3 Asymptotic Series  1.4 Algebraic and Analytic Operations  1.5 Existence of Functions with a Given Asymptotic Expansion  1.6 Asymptotic Power Series in a Complex Variable  1.7 Asymptotic Approximation of Partial Sums  1.8 The EulerMaclaurin Summation Formula  1.9 Exercises  2 Introduction to the Theory of Distributions  2.1 Introduction  2.2 The Space of Distributions D?  2.3 Algebraic and Analytic Operations  2.4 Regularization, Pseudofunction and Hadamard Finite Part  2.5 Support and Order  2.6 Homogeneous Distributions  2.7 Distributional Derivatives of Discontinuous Functions  2.8 Tempered Distributions and the Fourier Transform  2.9 Distributions of Rapid Decay  2.10 Spaces of Distributions Associated with an Asymptotic Sequence  2.11 Exercises  3 A Distributional Theory for Asymptotic Expansions  3.1 Introduction  3.2 The Taylor Expansion of Distributions  3.3 The Moment Asymptotic Expansion  3.4 Expansions in the Space P?  3.5 Laplace's Asymptotic Formula  3.6 The Method of Steepest Descent  3.7 Expansion of Oscillatory Kernels  3.8 TimeDomain Asymptotics  3.9 The Expansion of f (?x) as ? ? ? in Other Cases  3.10 Asymptotic Separation of Variables  3.11 Exercises  4 Asymptotic Expansion of Multidimensional Generalized Functions  4.1 Introduction  4.2 Taylor Expansion in Several Variables  4.3 The Multidimensional Moment Asymptotic Expansion  4.4 Laplace's Asymptotic Formula  4.5 Fourier Type Integrals  4.6 TimeDomain Asymptotics  4.7 Further Examples  4.8 Tensor Products and Partial Asymptotic Expansions  4.9 An Application in Quantum Mechanics  4.10 Expansion of Kernels of the Type f (?x, x)  4.11 Exercises  5 Asymptotic Expansion of Certain Series Considered by Ramanujan  5.1 Introduction  5.2 Basic Formulas  5.3 Lambert Type Series  5.4 Distributionally Small Sequences  5.5 Multiple Series  5.6 Unrestricted Partitions  5.7 Exercises  6 Cesàro Behavior of Distributions  6.1 Introduction  6.2 Summability of Series and Integrals  6.3 The Behavior of Distributions in the (C) Sense  6.4 The Cesàro Summability of Evaluations  6.5 Parametric Behavior  6.6 Characterization of Tempered Distributions  6.7 The Space K?  6.8 Spherical Means  6.9 Existence of Regularizations  6.10 The Integral Test  6.11 Moment Functions  6.12 The Analytic Continuation of Zeta Functions  6.13 Fourier Series  6.14 Summability of Trigonometric Series  6.15 Distributional Point Values of Fourier Series  6.16 Spectral Asymptotics  6.17 Pointwise and Average Expansions  6.18 Global Expansions  6.19 Asymptotics of the Coincidence Limit  6.20 Exercises  7 Series of Dirac Delta Functions  7.1 Introduction  7.2 Basic Notions  7.3 Several Problems that Lead to Series of Deltas  7.4 Dual Taylor Series as Asymptotics of Solutions of Equations  7.5 Boundary Layers  7.6 Spectral Content Asymptotics  7.7 Exercises  References
 Dimensions
 unknown
 Edition
 Second edition.
 Extent
 1 online resource (xv, 451 pages 3 illustrations).
 File format
 unknown
 Form of item
 online
 Isbn
 9780817681302
 Isbn Type
 (electronic bk.)
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9780817681302
 Quality assurance targets
 unknown
 Reformatting quality
 access
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)853261332
 (OCoLC)ocn853261332
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