I. J. Schoenberg Selected Papers

445 Pages·1988·16.717 MB·English

by  I. J. Schoenberg (auth.), Carl de Boor (eds.)

Contemporary Mathematicians
Gian-Carlo Rota
Editor
Springer Science+Business Media, LLC
AN HOMAGE
TO
LEONHARD EULER
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(page 29).
Frontispiece from [114] Cardinal Spline Interpolation CBMS Regional Conference
Monograph No. 12, SIAM, 1973. Reprinted by permission of SIAM.
I.J. Schoenberg
Selected Papers
Volume 2
Edited by
Carl de Boor
Springer Science+Business Media, LLC 1988
I.J. Schoenberg
Carl de Boor (Editor)
University of Wisconsin-Madison
Madison, WI 53705
U.S.A.
Library of Congress Cataloging-in-Publication Data
Schoenberg, I.J.
[Selections. 1988]
Selected papers /I.J. Schoenberg ; edited by Carl de Boor.
p. cm.—(Contemporary mathematicians)
Includes bibliographies.
ISBN 978-1-4899-0435-5
1. Mathematics—Collected works. I. De Boor, Carl. II. Title.
III. Title: I.J. Schoenberg, selected papers. IV. Series.
QA3.S365A25 1988
510—dcl9 .
88 2860
CIP-Titelaufnahme der Deutschen Bibliothek
Schoenberg, Isaac J.:
Selected papers /1. J. Schoenberg. Ed. by Carl de Boor. —
Boston ; Basel : Birkhäuser.
(Contemporary mathematicians)
ISBN 978-1-4899-0435-5
NE: Schoenberg, Isaac J.: [Sammlung]
WG: 27 DBN 55.138120.5
6954/01 rr
WG: 27 DBN 88.021072.9 88.01.20
6954/02* rr
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© Springer Science+Business Media New York 1988
Originally published by Birkhäuser Boston Inc. in 1988
Softcover reprint of the hardcover 1st edition 1988
ISBN 978-1-4899-0435-5 ISBN 978-1-4899-0433-1 (eBook)
DOI 10.1007/978-1-4899-0433-1
Table of Contents
Volume 2
Table of Contents, Volume 1 . . . vii
Publications of I. J. Schoenberg . . ix
Cardinal splines
[31] Contributions to the problem of approximation of equidistant data by analytic
functions. Part A: On the problem of smoothing or graduation. A first class
of analytic approximation formulae . . . . . . . . . . . . . . . . . . . . . . 3
[32] Contributions to the problem of approximation of equidistant data by analytic
functions. Part B: On the problem of osculatory interpolation. A second class
of analytic approximation formulae . . . . . . . . . . . . . . . . . . . . . . 58
[110] Cardinal interpolation and spline functions IV. The exponential Euler splines . 88
[113] Cardinal interpolation and spline functions VII. The behavior of cardinal
spline interpolants as their degree tends to infinity ............. 111
[129] On the remainders and the convergence of cardinal spline interpolation for
almost periodic functions 137
C. de Boor: Cardinal splines 164
Smoothing
[48] On smoothing operations and their generating functions. 169
[76] Spline functions and the problem of graduation 201
Total positivity and variation diminution
[4] Uber variationsvermindernde line are Transformationen 207
[15] Zur Abzahlung der reellen Wurzeln algebraischer Gleichungen 216
[45] (With M. Aissen and A. M. Whitney), On the generating functions of totally
positive sequences I . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
[90] (With M. Marsden), On variation diminishing spline approximation
methods .......................... . 247
S. Karlin: Total positivity and variation diminishing transformations 269
P6lya frequency functions
[43] On P6lya frequency functions. I. The totally positive functions and their
Laplace transforms . . . . . . . . . . . . . . . . . . . . . . . . . . 277
[39] On P6lya frequency functions. II. Variation diminishing integral operators
of the convolution type ........................ 321
[47] (With Anne Whitney), On P6lya frequency functions. III. The positivity
of translation determinants with an application to the interpolation problem
by spline curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
v
[86] (With H. B. Curry), On P6lya frequency functions. N. The fundamental
spline functions and their limits. . . . . . . . . 347
S. Karlin: P6lya frequency functions and sequences 384
The variational approach to splines
[72] Spline interpolation and best quadrature formulae 391
[75] On best approximations of linear operators 397
[80] On interpolation by spline functions and its minimal properties 407
C. de Boor: The variational approach to splines . 428
Hermite-Birkhoff interpolation
[89] On Hermite-Birkhoff interpolation ... 432
G.G. Lorentz: Schoenberg's work on Hermite-Birkhoff interpolation 438
Permissions 441
vi Table of Contents, Volume 2
Volume 1
C. de Boor: Foreword ... v
Table of Contents, Volume 2 ix
Publications of 1. J. Schoenberg . xi
1. J. Schoenberg: A brief account of my life and work 1
Number theory
[1] Uber die asymptotische Verteilung reeller Zahlen mod 1 . 13
[18] On asymptotic distributions of arithmetical functions .43
[22] Regular simplices and quadratic forms 59
P. Erdos: Commentary 67
Linear inequalities
[7] On finite and infinite completely monotonic sequences . . . . . . . 70
[50] (With T. S. Motzkin), The relaxation method for linear inequalities 75
J.-L. Goffin: The relaxation method for linear inequalities .87
Metric geometry
[16] Remarks to Maurice Frechet's article 'Sur la definition axiomatique d'une
classe d'espace distancies vectoriellement applicable sur l'espace de Hilbert' . 90
[25] Metric spaces and positive definite functions . . . . . . . . . 110
[26] Metric spaces and completely monotone functions 115
[28] (With J. von Neumann), Fourier integrals and metric geometry 146
[29] Positive definite functions on spheres . . . 172
[49] On a theorem of Kirzbraun and Valentine . 186
S. Cambanis and D. Richards: Metric geometry . 189
R. Askey: Commentary on a footnote . . . . . 192
Real analysis
[24] On the Peano curve of Lebesgue . . . . . . . . . . . . . . . . . . 197
[51] An isoperimetric inequality for closed curves convex in even-dimensional
Euclidean spaces . . . . . . . . . . . . . . . . . . . . . 199
[70] On the Besicovitch-Perron solution of the Kakeya problem 221
Complex analysis
[44] (With T. S. Motzkin)' On lineal entire functions of n complex variables 229
[53] On the zeros of the generating functions of multiply positive sequences and
functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 239
[55] (With G. P6Iya), Remarks on de la Vallee Poussin means and convex conformal
maps of the circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
vii
[60] (With B. Epstein), On a conjecture concerning schlicht functions 305
[106] Norm inequalities for a certain class of Coo functions 308
S. Ruscheweyh: The P6lya-Schoenberg conjecture ..... 317
Extremum problems
[100] (With A. Cavaretta), Solution of Landau's problem concerning higher
derivatives on the halfline . . . . . . . . . . . . . . . . . 320
[105] The perfect B-splines and a time-optimal control problem 335
[141] The Landau problem I. The case of motions on sets . . . 350
[149] The Landau problem II. The case of motions on curves 361
[150] The Landau problem III. Motions on special curves and time-optimal
control problems ......................... 373
History
[157] On polynomial interpolation at the points of a geometric progression 391
Permissions 405
viii Table of Contents, Volume I
Publications of I. J. Schoenberg
1 * Uber die asymptotische Verteilung reeller Zahlen mod 1, Math. Z. 28 (1928), 171-199.
a
2. Sur un theoreme de Steiner relatif la quadrature des courbes roulettes, Ann. Sci.
Univ. Jassy 16 (1930),6--13.
3. Uber total monotone Folgen mit stetiger Belegungsfunktion, Math. Z. 30 (1929),761-
767.
4* Uber variationsvermindernde lineare Transformationen, Math. Z. 32 (1930),321-328.
5. (With G. A. Bliss), On separation, comparison and oscillation theorems for self-adjoint
systems of linear second order differential equations, Amer. J. Math. LIII (1931), 781-
800.
6. The minimizing properties of geodesic arcs with conjugate end points, Ann. of Math.
(2) 32 (1931),763-776.
7* On finite and infinite completely monotonic sequences, Bull. Amer. Math. Soc. (Feb.
1932), 72-76.
8. On finite-rowed systems of linear inequalities in infinitely many variables. I, Trans.
Amer. Math. Soc. 34 (1932), 594-619.
9. On finite-rowed systems of linear inequalities in infinitely many variables. II, Trans.
Amer. Math. Soc. 35 (1932), 452-478.
10. (With G. A. Bliss), On the derivation of necessary conditions for the problem of Bolza,
Bull. Amer. Math. Soc. (Dec. 1932),858-864.
11. Some applications of the calculus of variations to Riemannian geometry, Ann. of Math.
33 (1932), 485-495.
12. Convex domains and linear combinations of continuous functions, Bull. Amer. Math.
Soc. (Apr. 1933), 273-280.
13. (With T. H. Hildebrandt), On linear functional operations and the moment problem
for a finite interval in one or several dimensions, Ann. of Math. 34 (1933),317-328.
14. A remark on the preceding note by Bochner, Bull. Amer. Math. Soc. (Apr. 1934),
277-278.
15* Zur Abziihlung der reellen Wurzeln algebraischer Gleichungen, Math. Z. 38 (1934),
546-564.
16* Remarks to Maurice Frechet's article 'Sur la definition axiomatique d'une classe
d'espace distancies vectoriellement applicable sur l'espace de Hilbert,' Ann. of Math.
36 (1935), 724-732.
17. On the zeros of the successive derivatives of integral functions, Proc. Nat. Acad. Sci.
21 (1935),674-676.
18* On asymptotic distributions of arithmetical functions, Trans. Amer. Math. Soc. 39
(1936), 315-330.
19. Extensions of theorems of Descartes and Laguerre to the complex domain, Duke Math.
J. 2 (1936),84-94.
20. On certain two-point expansions of integral functions of exponential type, Bull. Amer.
Math. Soc. (1936), 284-288.
21. On the zeros of successive derivatives of integral functions, Trans. Amer. Math. Soc.
40 (1936), 12-23.
22* Regular simplices and quadratic forms, J. London Math. Soc. 12 (1937),48-55.
ix