Selected papers
著者
書誌事項
Selected papers
（Springer Collected Works in Mathematics）
Springer, 2013, c2005
- 1 : softcover
- 2 : softcover
- タイトル別名
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Selected papers I
Selected papers II
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注記
"Reprint of the 2005 edition"--T.p. of 1-2
Includes bibliographical references
内容説明・目次
- 巻冊次
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2 : softcover ISBN 9781461494317
内容説明
A renowned mathematician who considers himself both applied and theoretical in his approach, Peter Lax has spent most of his professional career at NYU, making significant contributions to both mathematics and computing. He has written several important published works and has received numerous honors including the National Medal of Science, the Lester R. Ford Award, the Chauvenet Prize, the Semmelweis Medal, the Wiener Prize, and the Wolf Prize. Several students he has mentored have become leaders in their fields.
Two volumes span the years from 1952 up until 1999, and cover many varying topics, from functional analysis, partial differential equations, and numerical methods to conservation laws, integrable systems and scattering theory. After each paper, or collection of papers, is a commentary placing the paper in context and where relevant discussing more recent developments. Many of the papers in these volumes have become classics and should be read by any serious student of these topics. In terms of insight, depth, and breadth, Lax has few equals. The reader of this selecta will quickly appreciate his brilliance as well as his masterful touch. Having this collection of papers in one place allows one to follow the evolution of his ideas and mathematical interests and to appreciate how many of these papers initiated topics that developed lives of their own.
目次
- Scattering Theory in Euclidean Space.- The Wave Equation in Exterior Domains.- Exponential Decay of Solutions of the Wave Equation in the Exterior of a Star-Shaped Obstacle.- Scattering Theory.- Decaying Modes for the Wave Equation in the Exterior of an Obstacle.- On the Scattering Frequencies of the Laplace Operator for Exterior Domains.- Commentary on Part V.- Scattering Theory for Automorphic Functions.- Translation Representations for the Solution of the Non-Euclidean Wave Equation.- Scattering Theory for Automorphic Functions.- Translation Representations for the Solution of the Non-Euclidean Wave Equation. II.- The Asymptotic Distribution of Lattice Points in Euclidean and Non-Euclidean Spaces.- A Local Paley-Wiener Theorem for the Radon Transform of L 2 Functions in a Non-Euclidean Setting.- Translation Representations for Automorphic Solutions of the Wave Equation in Non-Euclidean Spaces. I.- Translation Representations for Automorphic Solutions of the Wave Equation in Non-Euclidean Spaces. II.- Translation Representations for Automorphic Solutions of the Wave Equation in Non-Euclidean Spaces. III.- Translation Representation for Automorphic Solutions of the Wave Equation in Non-Euclidean Spaces, IV.- Translation Representations for Automorphic Solutions of the Wave Equation in Non-Euclidean Spaces
- the Case of Finite Volume.- Commentary on Part VI.- Functional Analysis.- A Stability Theorem for Solutions of Abstract Differential Equations, and Its Application to the Study of the Local Behavior of Solutions of Elliptic Equations.- A Phragmen-Lindeloef Theorem in Harmonic Analysis and Its Application to Some Questions in the Theory of Elliptic Equations.- Translation Invariant Spaces.- The Time Delay Operator and a Related Trace Formula.- The Translation Representation Theorem.- Trace Formulas for the Schroedinger Operator.- Commentary on Part VII.- Analysis.- Approximation of Measure Preserving Transformations.- On the Factorization of Matrix-Valued Functions.- A Short Path to the Shortest Path.- Change of Variables in Multiple Integrals.- Change of Variables in Multiple Integrals II.- Commentary on Part VIII.- Algebra.- On Matrices Whose Real Linear Combinations are Nonsingular.- Correction to "On Matrices Whose Real Linear Combinations are Nonsingular".- On Sums of Squares.- The Multiplicity of Eigenvalues.- On the Discriminant of Real Symmetric Matrices.- Commentary on Part IX.
- 巻冊次
-
1 : softcover ISBN 9781461494324
内容説明
A renowned mathematician who considers himself both applied and theoretical in his approach, Peter Lax has spent most of his professional career at NYU, making significant contributions to both mathematics and computing. He has written several important published works and has received numerous honors including the National Medal of Science, the Lester R. Ford Award, the Chauvenet Prize, the Semmelweis Medal, the Wiener Prize, and the Wolf Prize. Several students he has mentored have become leaders in their fields.
Two volumes span the years from 1952 up until 1999, and cover many varying topics, from functional analysis, partial differential equations, and numerical methods to conservation laws, integrable systems and scattering theory. After each paper, or collection of papers, is a commentary placing the paper in context and where relevant discussing more recent developments. Many of the papers in these volumes have become classics and should be read by any serious student of these topics. In terms of insight, depth, and breadth, Lax has few equals. The reader of this selecta will quickly appreciate his brilliance as well as his masterful touch. Having this collection of papers in one place allows one to follow the evolution of his ideas and mathematical interests and to appreciate how many of these papers initiated topics that developed lives of their own.
目次
- Partial Differential Equations.- On the existence of Green's Function.- Parabolic Equations.- On Cauchy's Problem for Hyperbolic Equations and the Differentiability of Solutions of Elliptic Equations.- The Propagation of Discontinuities in Wave Motion.- Asymptotic Solutions of Oscillatory Initial Value Problems.- Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations.- On Stability for Difference Schemes
- a Sharp Form of Garding's Inequality.- An Example of Huygens' Principle.- A Simple One-dimensional Model for the Three-dimensional Vorticity Equation.- Commentary on Part I.- Difference Approximations to PDE.- Survey of the Stability of Linear Finite Difference Equations.- On the Stability of Difference Approximations to Solutions of Hyperbolic Equations With Variable Coefficients.- The Computation of Discontinuous Solutions of Linear Hyperbolic Equations.- Accuracy and Resolution in the Computation of Solutions of Linear and Nonlinear Equations.- Commentary on Part II.- Hyperbolic Systems of Conservation Laws.- Weak Solutions of Nonlinear Hyperbolic Equations and Their Numerical Computation.- Hyperbolic Systems of Conservation Laws II.- Systems of Conservation Laws.- Difference Schemes for Hyperbolic Equations with High Order of Accuracy.- Shock Waves and Entropy.- Systems of Conservation Equations with a Convex Extension.- Positive Schemes for Solving Multi-Dimensional Hyperbolic Systems of Conservation Laws.- Commentary on Part III.- Integrable Systems.- Integrals of Nonlinear Equations of Evolution and Solitary Waves.- Periodic Solutions of the KdV Equation.- Almost Periodic Solutions of the KdV Equation.- The Small Dispersion Limit of the Korteweg-de Vries Equation. I.- The Small Dispersion Limit of the Korteweg-de Vries Equation. II.- The Small Dispersion Limit of the Korteweg-deVries Equation. III.- On Dispersive Difference Schemes. I.- Dispersive Approximations in Fluid Dynamics.- Commentary on Part IV.
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