Anniversary Volume on Approximation Theory and Functional Analysis

601 Pages·1984·12.976 MB·English

by  Bl. Sendov (auth.), Prof. P. L. Butzer, Priv.-Doz. Dr. R. L. Stens, Prof. B. Sz.-Nagy (eds.)

ISNM65:
International Series of Numerical Mathematics
Internationale Schriftenreihe zur Numerischen Mathematik
Serie internationale d' Analyse numerique
Vol. 65
Edited by
Ch. Blanc, Lausanne; A. Ghizzetti, Roma;
R. Glowinski, Paris; G. Golub, Stanford;
P. Henrici, Ziirich; H. O. Kreiss, Pasadena;
A. Ostrowski, Montagnola; J. Todd, Pasadena
Springer Basel AG
Anniversary Volume on
Approximation Theory
and Functional Analysis
Edited by
P. L. Butzer, Aachen
R. L. Stens, Aachen
B. Sz.-Nagy, Szeged
1984
Springer Basel AG
Proceedings of the Conference Held at the Mathematical Research Institute
at Oberwolfach, Black Forest, July 30 - August 6, 1983
Editors
Prof. P. L. Butzer
Rhein.-Westf. Techn. Hochschule Aachen
Lehrstuhl A fUr Mathematik
Templergraben 55
0-5100 Aachen (FRG)
Priv.-Ooz. Or. R. L. Stens
Rhein.-Westf. Techn. Hochschule Aachen
Lehrstuhl A fUr Mathematik
Templergraben 55
0-5100 Aachen (FRG)
Prof. B. Sz.-Nagy
J6zsef Attila University
Aradi vertanuk tere 1
H-6720 Szeged (Hungary)
Library of Congress Cataloging in Publication Data CIP-Kurztitelaufnahme der Deutsmen Bil
Anniversary volume on approximation theory and Anniversary volume on approximation th~
functional analysis. functional analysis : proceedings of the cc
(International series of numerical mathematics ; held at the Math. Research Inst. at Oberwe
v.65) Black Forest, July 30 - August 6, 1983 I
Lectures given at the International Conference on ed. by P. L. Butzer ... -
Approximation Theory and Functional Analysis. Basel ; Boston ; Stuttgart : Birkhiiuser,
1. Approximation theory - - Congresses. 2. Functional (International series of numerical
analysis - - Congresses. I. Butzer, Paul Leo, 1928- mathematics ; Vol. 65)
II. Stens, R. L., 1948- III. Szokefalvi-Nagy,
Bela,1913- IV. International Conference on
Approximation Theory and Functional Analysis (1983: NE: Butzer, Paul L. [Hrsg.]; Mathematisd
Oberwolfach Mathematical Research Institute) Forschungsinstitut (Oberwolfach); GT
V. Mathematisches Forschungsinstitut Oberwolfach.
VI. Series.
QA221.A538 1984 511'.4 84-18451
All rights reserved.
No part of this publication may be reproduced, stored in a retrieval system, or
transmitted in any form or by any means, electronic, mechanical, photocopying,
recording or otherwise, without the prior permission of the copyright owner.
© 1984 Springer Basel AG
Originally published by Birkhiiuser Verlag Basel in 1984.
Softcover reprint of the hardcover I st edition 1984
ISBN 978-3-0348-5434-4 ISBN 978-3-0348-5432-0 (eBook)
DOI 10.1007/978-3-0348-5432-0
Lyubomir Diev Ralph Phillips
Born on April 20, 1913 ,in Veliko Tarnovo Born on June 23,1913 in Los Angeles
Bela SzoKefalvi-Nagy Adriaan Cornelis Zaanen
Born on July 29, 1913 in Kolozsvar Born on June 14, 1913 in Rotterdam
6
Previous Conferences on Approximation Theory,
Functional Analysis and Related Topics
held since 1963 at the Oberwolfach Mathematical Research Institute and conducted from
Aachen, in collaboration with a colleague from abroad since 1968
1. On Approximation Theory, August 4-10,1963. (Eds. ofthe Proceedings: P.L. Butzer,
J. Korevaar; ISNM, vol. 5, Birkhauser Verlag, Basel 1964 (second edition 1972), XVI
+ 261 pages)
2. Arbeitstagung tiber Approximationstheorie, March 1-8, 1964. (Without Proceedings)
3. Harmonische Analysis und Integraltransformationen, August 2-10, 1965. (Without
Proceedings)
4. Abstract Spaces and Approximation, July 18-27, 1968. (Eds.: P.L. Butzer, B. Sz.
Nagy; ISNM, vol. 10, Birkhauser Verlag, Basel 1969,423 pages)
5. Linear Operators and Approximation I, August 14-22,1971. (Eds.: P.L. Butzer, J.-P.
Kahane, B. Sz.-Nagy; ISNM, vol. 20, Birkhauser Verlag, Basel 1972,506 pages)
6. Linear Operators and Approximation II, March 30-April 6, 1974. (Eds.: P.L. Butzer,
B. Sz.-Nagy; ISNM, vol. 25, Birkhauser Verlag, Basel 1974, XX + 588 pages)
7. Linear Spaces and Approximation, August 20-27, 1977. (Eds.: P.L. Butzer, B. Sz.
Nagy; ISNM, vol. 40, Birkhauser Verlag, Basel 1978, 685 pages)
8. Functional Analysis and Approximation, August 9-16, 1980. (Eds.: P.L. Butzer, B.
Sz.-Nagy, E. Goriich; ISNM, vol. 60, Birkhauser Veriag, Basel 1981, 482 pages)
Anniversary Commemorations
This volume forms a record of the lectures given at the international Conference on
Approximation Theory and Functional Analysis held at the Oberwolfach Mathematical
Research Institute from 30. July to 6. August 1983. It commemorates at the same time
several anniversaries:
(i) The 70th anniversary in 1983 ofthe birth of four of our many Oberwolfach participants
during the past years, namely Professors L. Iliev (Sofia), R. Philipps (Stanford), B.
Sz6kefalvi-Nagy (Szeged) and A.c. Zaanen (Leiden). Consequently the articles of
this volume are dedicated to these four distinguished mathematicians as a token of
friendship and esteem.
(ii) The 20th anniversary of the Oberwolfach conference "On Approximation Theory"
held August 4-10, 1963. This inaugurated a series of conferences conducted from
Aachen, in collaboration with Bela Sz.-Nagy since 1968, and in 1968 also with J.-P.
Kahane (Paris). It was the first to deal with approximation theory in the Western
world.l)
The conference in 1963 was also the first of any of the Oberwolfach Conferences
(since the founding of the Institute in 1944) to be published in an accessible volume of
proceedings, making the results -lectures, problems, remarks, etc. - available to the
wider mathematical community. The proceedings of 1963 were edited by P.L. Butzer
and J. Korevaar (Amsterdam), printed at Professor Barner's chair in Freiburg i.Br.,
and published by Birkhiiuser, Basel.
At this point we extend our sincere thanks to Professor Martin Barner, Director of
the Oberwolfach Mathematical Research Institute, for the outstanding cooperation during
these twenty years. He and his team at Freiburg and Oberwolfach, with Mr. H.G. For
stendorf as administrative official, have not only helped with their expert planning and ad-'
1) A conference "On Numerical Approximation" had taken place in Madison, Wisc. on April 21-23, 1958
(Proc. edited by R.E. Langer; Univ. of Wisconsin Press. Madison 1959. x + 462 pp.). There also were two con
ferences in the USSR with associated proceedings. namely: "Investigations in Modern Problems of the Con
structive Theory of Funct." (Russ.) (Proc. First Conf. Constructive Theory Funct.; Leningrad Oct. 1959; V.1.
Smirnov. ed.), Gos. Izdat. Fiz.-Mat. Lit., Moscow 1961, 368 pp. and "Studies of Contemporary Problems of
Constructive Theory of Functions" (Russ.) (Proc. Second All-Union Conf. Constructive Theory Funct.; Baku
Oct. 8-13, 1962; 1.1. Ibragimov. ed.) Izdat. Akad. Nauk AzerbaidZan SSR, Baku 1965,638 pp.
8 Anniversary Commemorations
vice but have always provided the best possible facilities and surroundings to conduct such
conferences. There is no doubt that their interest and concern contributed substantially
towards making the conferences rewarding scientific experiences as well as memorable
social events for successive international groups of participants.
P.L. Butzer
Aachen
9
Preface
These Proceedings include 42 of the 49 invited conference papers, three papers sub
mitted subsequently, and a report devoted to new and unsolved problems based on two
special problem sessions and as augmented by later communications from the participants.
In addition, there are four short accounts that emphasize the personality of the scholars to
whom the proceedings are dedicated. Due to the large number of contributors, the length
of the papers had to be restricted.
This volume is again devoted to recent significant results obtained in approximation
theory, harmonic analysis, functional analysis, and operator theory. The papers solicited
include in addition survey articles that not only describe fundamental advances in their
subfields, but many also emphasize basic interconnections between the various research
areas. They tend to reflect the range of interests of the organizers and of their immediate
colleagues and collaborators.
The papers have been grouped according to subject matter into ten chapters. Chap
ter I, on operator theory, is devoted to certain classes of operators such as contraction,
hyponormal, and accretive operators, as well as to suboperators and semi groups of
operators. Chapter II, on functional analysis, contains papers on function spaces, algebras,
ideals, and generalized functions. Chapter III, on abstract approximation, is concerned
with the comparison of approximation processes, the gliding hump method, certain inter
polation spaces, and n-widths. Whereas Chapter IV deals with approximation of functions
of one or two real variables by linear approximation processes or with best approximation
of those functions by polynomials, also on disjoint intervals, Chapter V is mainly devoted
to the approximation of functions of a complex variable, including the Shannon sampling
theorem. More or less classical interpolation problems are handled in Chapter VI, and
orthogonal polynomials and functions, abstract harmonic analysis and their applications
are dealt with in Chapter VII. Chapter VIII includes papers on ordinary and partial dif
ferential equations, and on difference equations, in particular concerning the approxima
tion of solutions and, finally, Chapter IX contains papers on probability theory and statis
tics, and a result in integral geometry. The volume closes with Chapter X on new and un
solved problems.
The number of mathematicians, in East and West, who are actively engaged in ap
proximation theory and related topics has very much increased since 1963. This fact and
our policy to include a number of mathematicians who have not attended our previous con
ferences, as well as the limited capacity of the Oberwolfach Institute, explain why we were
unfortunately unable to reinvite all those who had participated in some of the foregoing