(1988).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. |
Contents
Cber die asymptotische Verteilung reeller Zahlen mod 1 | 13 |
FUNCTIONS | 43 |
REGULAR SIMPLICES AND QUADRATIC FORMS | 59 |
Comment ary | 67 |
LINEAR INEQUALITIES | 69 |
ON FINITE AND INFINITE COMPLETELY MONOTONIC SEQUENCES | 70 |
THE RELAXATION METHOD FOR LINEAR INEQUALITIES | 75 |
The relaxation method for linear inequalities | 87 |
ON THE PEANO CURVE OF LEBESGUE | 197 |
CONVEX IN EVENDIMENSIONAL EUCLIDEAN SPACES | 199 |
On the BesicovitchPerron Solution of the Kakeya Problem | 221 |
COMPLEX ANALYSIS | 227 |
ON LINEAL ENTIRE FUNCTIONS OF w COMPLEX VARIABLES | 229 |
ON THE ZEROS OF THE GENERATING FUNCTIONS OF MULTIPLY POSITIVE SEQUENCES AND FUNCTIONS1 | 239 |
AND CONVEX CONFORMAL MAPS OF THE CIRCLE | 265 |
ON A CONJECTURE CONCERNING SCHLICHT FUNCTIONS1 | 305 |
METRIC GEOMETRY | 89 |
AXIOMATIQUE DUNE CLASSE DESPACE DISTANCES VECTOR IELLEMENT APPLICABLE SUR LESPACE DE HILBERT1 | 90 |
METRIC SPACES AND POSITIVE DEFINITE FUNCTIONS | 100 |
METRIC SPACES AND COMPLETELY MONOTONE FUNCTIONS1 | 115 |
FOURIER INTEGRALS AND METRIC GEOMETRY | 146 |
POSITIVE DEFINITE FUNCTIONS ON SPHERES | 172 |
ON A THEOREM OF KIRZBRAUN AND VALENTINE | 186 |
Metric geometry | 189 |
Commentary on a footnote | 192 |
REAL ANALYSIS | 195 |
The P61yaSchoenberg Conjecture | 317 |
SOLUTION OF LANDAUS PROBLEM CONCERNING HIGHER DERIVATIVES ON THE HALFLINE | 320 |
THE PERFECT 5SPLINES AND A TIMEOPTIMAL CONTROL PROBLEM | 335 |
The case of motions on sets | 350 |
The case of motions on curves | 361 |
Motions on special curves and timeoptimal control problems | 373 |
HISTORY | 389 |
On polynomial interpolation at the points of a geometric progression | 391 |
Permissions | 405 |
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Amer approximation assume B-splines bounded cardinal spline class of functions closed curve coefficients conclude condition conjecture continuous converges convex Corollary defined denote distribution function dy(u entire function equation euclidean space Euler splines F(Em F²(t finite folgt following theorem formula Fourier function F(t geometric hence Hilbert space I. J. SCHOENBERG identical imbeddable implies inequality infinite integral interpolation interval isometrically k-times positive Landau motion Landau problem Lemma linear Math Mathematics matrix metric space metric transform monotone functions non-decreasing non-negative obtain p₁ paper perfect spline Pipk points polygon polynomial positive definite functions power series proof of Theorem prove quadratic form relation remark result Satz screw function screw line sequence sin² solution spline functions stetig Theorem theory totally positive unit circle values vanish variables variation diminishing vector Zahlen zeros
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Page xvi - On the remainders and the convergence of cardinal spline interpolation for almost periodic functions.