Beschreibung
This memorial volume is dedicated to E. B. Christoffel on the occasion of the 150th anniversary of his birth. Its aim is, on the one hand, to present the life of Christoffel and the scientific milieu in which he worked and, on the other hand, to present a survey of his work not only in its historical context but especially in the frame of contemporary mathematics and physics. For one thing, this book contains expanded versions of the twelve invited lectures given at the International Christoffel Symposium, held on November 8- 11, 1979 at Aachen and Monschau. For another, the scope of these papers has been broadened by soliciting some fourty-five additional invited articles, concerned either with further aspects of the work of Christoffel or with specia lized topics in fields in which Christoffel had worked. This should give the reader a greater opportunity to appreciate the richness of Christoffel's contributions to the mathematical and physical sciences, and not only its immediate impact but also its subsequent infiuence. It can be discerned that Christoffel did basic work not only in differential geometry or, better still, in classical tensor analysis, thereby supplying the mathematical foundations of Einstein's theory of general relativity, but also in a variety of other areas of mathematics. The scope of Christoffel's work can be appreciated from the following synopsis of the thirteen chapters into which the festschrift is divided. Chap.
Autorenporträt
InhaltsangabeChristoffel and His Time.- An Outline of the Life and Work of E.B. Christoffel (1829-1900).- Zur Genealogie E. B. Christoffels.- Christoffel und die Mathematik an der polytechnischen Schule Zürich.- Die Berliner Gewerbeakademie und ihre Mathematiker.- Das Mathematische Seminar der Universität Strassburg 1872-1900.- Gauss-Christoffel Quadrature Formulae.- A Survey of Gauss-Christoffel Quadrature Formulae.- Numeri di Christoffel e polinomi s-ortogonali.- Orthogonal Polynomials, Continued Fractions and Padé Approximation.- Die Bedeutung der Christoffelschen Summenformel für die Entwicklung nach Orthogonalpolynomen.- Orthogonal Polynomials which Satisfy Second Order Differential Equations.- Über Orthogonalpolynome mit besonderen Eigenschaften.- The Work of E.B. Christoffel on the Theory of Continued Fractions.- A Priori Truncation Error Estimates for Stieltjes Fractions.- Generalisations of Padé Approximation for Chebyshev and Fourier Series.- An Asymptotic, Padé Approximant Method for Legendre Series.- Christoffel-Schwarz Transformation and Conformal Representation.- Die Bedeutung der Arbeiten Christoffels für die Funktionentheorie.- Remarks on the Schwarz-Christoffel Transformation.- Computer Application of the Schwarz-Christoffel Transformation.- Regularity Properties of Solutions of Elliptic Equations Near Corners.- Das logarithmische Potential und die konforme Abbildung mehrfach zusammenhängender Gebiete.- Theta Functions, Automorphic Functions and Riemann Surfaces.- On Automorphic Functions.- Semigroups of Holomorphic Maps of a Riemann Surface into itself which are Homomorphs of the Set of Positive Reals Considered Additively.- Bemerkungen zur isometrischen Verheftung ebener Gebiete.- Eine Bemerkung zu Andrianovs expliziten Formeln für die Wirkung der Heckeoperatoren auf Thetareihen.- Schottky's Invariant and Quadratic Forms.- Differential Equations, Potential Theory.- A propos d'un travail de Christoffel sur les équations différentielles.- Über die Beiträge Christoffels zur Potentialtheorie.- Application d'un Théorème de Hörmander à l'Etude des Singularités des Problèmes aux Limites Hyperboliques.- On Fundamental Systems of Differential Semi-Invariants in Several Variables.- Parabolicity and the Riemann Theorem.- On the Structure of the Set of Eigenfunctions of Certain Irregular Boundary Problems.- Shock Waves, Continuum Mechanics.- Historischer Überblick zur mathematischen Theorie von Unstetigkeitswellen seit Riemann und Christoffel.- G. Herglotz' Behandlung von Beschleunigungswellen in seiner Vorlesung 'Mechanik der Kontinua' angewandt auf die Stosswellen von Christoffel.- Unstetigkeitsflächen in der Kontinuumsmechanik.- Riemannian Geometry, Submanifolds.- Die Bedeutung von Christoffel für die Geometrie.- E. B. Christoffels Weg zum absoluten Differentialkalkül und sein Beitrag zur Theorie des Krümmungstensors.- Une caractérisation purement métrique des variétés Riemanniennes à courbure constante.- Immersions et repères mobiles.- The Euclidean Laplacian.- Invariant Theory, Differential Operators and Field Physics.- Christoffel und die Invariantentheorie.- Christoffel's Work on the Equivalence Problem for Riemannian Spaces and Its Importance for Modem Field Theories of Physics.- Some Characterizations of Differential Operators on Vector Bundles.- Connections in Generalized Gauge Fields.- Remarks on the Cauchy Problem for the Maxwell Equations in a Curved Space-Time.- Affine and Projective Structures, Nonlinear Differential Geometry.- Die Bedeutung Christoffelscher Zusammenhänge in der affinen Differentialgeometrie.- On Projective Covariant Differentiation.- Generic Minimal Submanifolds with Flat Normal Connection.- Über die Verallgemeinerung der Christoffelschen Übertragungstheorie in Linienelementenräumen.- Die Verallgemeinerung Christoffelscher Zusammenhänge in der nichtlinearen Differentialgeometrie.- G-Spaces, Convex Bodies and Foundations.- Symmetric Spaces and Ellipses.- Zum Beweis eines Eindeutigkeitssatzes von A.D.
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