Selected Papers II

ISBN-13: 9781461494317 / Angielski / Miękka / 2013 / 591 str.

Peter D. Lax; Peter Sarnak; Andrew J. Majda

Opis

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.

Recenzje

From the reviews:

"For the 2 volumes of the Selecta, 59 papers of P.D. Lax were chosen and reprinted in order to represent his main achievements. The editors qualify the papers as 'classics' and state: 'their impact continues to be felt both explicitly and implicitly in current research'. ... let me mention that the two Selecta volumes contain further highly original ideas ... ." (Norbert Ortner, Mathematical Reviews, Issue 2006 k)

"Since Peter Lax was chosen as the recipient of the 2005 Abel Prize, it's hardly necessary to say that his work is important. Libraries should consider his Selected Papers an essential acquisition. ... This second volume includes many papers on scattering theory, a few on functional analysis, and several others ... under 'analysis' and 'algebra'." (Fernando Q. Gouvêa, MathDL, October, 2005)

Spis treści

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 Phragmén-Lindelöf 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.

O autorze

A renowned mathematician who considers himself both applied and theoretical in his approach, Peter D. 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.