I.J. Schoenberg Selected Papers

ISBN-13: 9781461284116 / Angielski / Miękka / 2012 / 406 str.

C. De Boor

Opis

These seleeta contain 761 of the more than 2600 pages of 1. J. Schoenberg's published articles. The selection made and the grouping in which the papers are presented here reflect most strongly Schoenberg's wishes. The first volume of these seleeta is drawn from Schoenberg's remarkable work on Number Theory, Positive Definite Functions and Metric Geometry, Real and Complex Analysis, and on the Landau Problem. Schoenberg's fundamental papers on Total Pos- itivity and Variation Diminution, on P6lya Frequency functions and sequences, and on Splines, especially Cardinal Splines, make up the second volume. In addition, various commentaries have been provided. Lettered references in these refer to items listed alphabetically at the end of each commentary. Numbered references refer to the list of Schoenberg's publications to be found in each volume. Those included in these seleeta are starred. It has been an honor to have been entrusted with the editorial work for these seleeta. I am grateful to the writers of the various commentaries for their illuminating contributions and to Richard Askey for solid advice.

Spis treści

A brief account of my life and work.- A brief account of my life and work.- Number theory.- [1] Über die asymptotische Verteilung reeller Zahlen mod 1.- [18] On asymptotic distributions of arithmetical functions.- [22] Regular simplices and quadratic forms.- Commentary.- Linear inequalities.- [7] On finite and infinite completely monotonic sequences.- [50] (With T. S. Motzkin), The relaxation method for linear inequalities.- The relaxation method for linear inequalities.- Metric geometry.- [16] Remarks to Maurice Fréchet’s article’ sur la définition axiomatique d’une classe d’espace distanciés vectoriellement applicable sur l’espace de Hilbert’.- [25] Metric spaces and positive definite functions.- [26] Metric spaces and completely monotone functions.- [28] (With J. von Neumann), Fourier integrals and metric geometry.- [29] Positive definite functions on spheres.- [49] On a theorem of Kirzbraun and Valentine.- Metric geometry.- Commentary on a footnote.- Real analysis.- [24] On the Peano curve of Lebesgue.- [51] An isoperimetric inequality for closed curves convex in even-dimensional Euclidean spaces.- [70] On the Besicovitch-Perron solution of the Kakeya problem.- Complex analysis.- [44] (With T. S. Motzkin), On lineal entire functions of n complex variables.- [53] On the zeros of the generating functions of multiply positive sequences and functions.- [55] (With G. Pólya), Remarks on de la Vallée Poussin means and convex conformai maps of the circle.- [60] (With B. Epstein), On a conjecture concerning schlicht functions.- [106] Norm inequalities for a certain class of C? functions.- The Pólya-Schoenberg conjecture.- Extremum problems.- [100] (With A. Cavaretta), Solution of Landau’s problem concerning higher derivatives on the halfline.- [105] The perfect B-splines and a time-optimal control problem.- [141] The Landau problem I. The case of motions on sets.- [149] The Landau problem II. The case of motions on curves.- [150] The Landau problem III. Motions on special curves and time-optimal control problems.- History.- [157] On polynomial interpolation at the points of a geometric progression.- Permissions.