Table Of ContentProceedings of the Second ISAAC Congress
International Society for Analysis, Applications and Computation
Volume 7
Managing Editor
Robert P. Gilbert
University of Delaware, U.S.A.
Advisory Board
Heinrich Begebr
Freie Universitat, Berlin, Germany
Antonio Fasano
University of Florence, Italy
Chung-Chun Yang
Hong Kong University of Science
& Technology, Hong Kong
The titles published in this series are listed at the end of this volume.
Proceedings of
the Second
ISAAC Congress
Volume 1
This project has been executed with Grant No. 11-56 from
the Commemorative Association for
the Japan World Exposition (1970)
Edited by
Heinrich G.W. Begehr
Freie Universitiit, Berlin, Germany
Robert P. Gilbert
University of Delaware, Newark, Delaware, U.S.A.
and
Joji Kajiwara
Kyushu University, Fukuoka, Japan
KLUWER ACADEMIC PUBLISHERS
DORDRECHT I BOSTON I LONDON
A CJ.P. Catalogue record for this book is available from the Library of Congress.
ISBN-13:978-1-4613-7970-6 e-ISBN-13:978-1-4613-0269-8
DOl: 10.1007/978-1-4613-0269-8
Published by Kluwer Academic Publishers,
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Preface
This book is the Proceedings of the Second ISAAC Congress.
ISAAC is the acronym of
the International Society for Analysis,
its Applications and Computation.
The president of ISAAC is Professor Robert P. Gilbert, the second
named editor of this book, e-mail: [email protected].
The Congress is world-wide valued so highly that an application for
a grant has been selected and this project has been executed with Grant
No. 11-56 from
*the Commemorative Association for
the Japan World Exposition (1970).
The finance of the publication of this book is exclusively the said Grant
No. 11-56 from *. Thus, a pair of each one copy of two volumes of
this book will be sent to all contributors, who registered at the Second
ISAAC Congress in Fukuoka, free of charge by the Kluwer Academic
Publishers.
Analysis is understood here in the broad sense of the word, includ
ing differential equations, integral equations, functional analysis, and
function theory. It is the purpose of ISAAC to promote analysis, its
applications, and its interaction with computation. With this objective,
ISAAC organizes international Congresses for the presentation and dis
cussion of research on analysis. ISAAC welcomes new members and
those interested in joining ISAAC are encouraged to look at the web
site
http://www. math. udel.edu/ gilbert/isaac/index.html
vi
and
http://www.math.fu-berlin.de/
rd/a g/isaac/newton/index.html.
The First ISAAC Congress was held at the University of Delaware,
Newark, Delaware, U. S. A. during June 1997. The Second ISAAC
Congress was held during August 1999 at Fukuoka Institute of Technol
ogy, Fukuoka, Japan.
As a novelty at the opening ceremony of the second congress ten
ISAAC Awards were handed over to those younger mathematicians who
were elected by an Award Committee. The awardees were
Daniele Andreucci (Roma, Italy; pdes, free boundary
problems),
Dao-Qing Dai (Guangzhou, China; complex methods in pdes, wavelet
analysis),
Le Hai Khoi (Hanoi, Vietnam; several complex variables, pdes),
P. Alexandrovich Krutitskii (Moscow, Russia; pdes,
applications) ,
Pei-Ghu Hu (Jinan, China; complex analysis),
Song-Ying Li (Irvine, Ca, USA; complex analysis of one and several
variables),
Stefano Marmi (Firence, Italy; dynamical systems, global
analysis),
Sergiy A. Plaksa (Kiev, Ukraine; complex analysis,
hypercomplex analysis),
Takashi Shioya (Fukuoka, Japan; differential geometry, global analysis),
Dachun Yang (Beijing, China; harmonic analysis, pdes).
The price was US $ 500 for those awardees who were attending the
congress. The fund for these awards was raised by the local organizers
Professor J. Kajiwara and Professor M. Nishihara, the representative
and the secretary-general of the said Grant No. 11-56 from • respec
tively, with which this project has been executed. The award committee
consisted of H. Begehr, A. Bourgeat, A.K. Briining, A. Fasano, C.H.
Fitzgerald, A. Jeffrey, J. Kajiwara, P. Tamrazov, C.C. Yang (Chair
man).
The ISAAC society will continue in encouraging young researchers in
analysis, its applications and computation by awarding prizes for high
quality research at its international congresses.
vii
The proceedings of the First ISAAC congress were published in 8
volumes. Only 4 of them have appeared in this series. The 8 volumes
are
Partial Differential and Integral Equations, eds. H.G.W. Begehr, R.P.
Gilbert, G.-C. Wen, this series 2 (1999).
Reproducing Kernels and their Applications, eds. S. Saitoh, R. Alpay,
J.A. Ball, T. Ohsawa, this series 3 (1999).
Recent Developments in Complex Analysis and Computer Algebra, eds.
R.P. Gilbert, J. Kajiwara, Y.S. Xu, this series 4 (1999).
Direct and Inverse Problems of Mathematical Physics, eds. R.P. Gilbert,
J. Kajiwara, Y.S. Xu, this series 5 (2000).
Inverse Problems, Tomography, and Image Processing. Proc. of ses
sions from 1. into congress of ISAAC. Ed. A.G. Ramm. Plenum Press,
New York, (1998).
Spectral and Scattering Theory. Proc. of sessions from 1. into congress
of ISAAC. Ed. A.G. Ramm. Plenum Press, New York, (1998).
Dirac Operators in Analysis. Eds. J. Ryan, D. Stuppa. Pitman Re
search Notes No. 394. Addison Wesley Longman, Harlow, (1998).
Orthogonal Polynomials and Computer Algebra. Eds. R.A. Askey, W.
Koepf, T.H. Koornwinder. Special issue of Journal of Symbolic Compu
tation. J. Symb. Comput. 28, (6) (1999).
Herein are the Proceedings of the Second Congress. From the Table
of Contents it is evident that Complex Analysis remains the dominant
research area of the attendees of the Congress. After that there is a
concentration in Real Analysis, Numerical and Computational Mathe
matics, and also Applied Mathematics. In the area of Complex Analysis
there are many sub-areas such as Hardy Spaces, Riemann-Hilbert prob
lems, hyperanalytic function theory, conformal mappings, Nevanlinna
theory, meromorphic functions, complex dynamics, Riemann surfaces,
entire functions, quasianalytic functions, and Bergman spaces, to name
a few. There is, of course, some overlap of topics. For instance, in the
area of differential equations which normally belongs to Real Analysis
there is also the Function Theoretic school; moreover, we will find nu
merous Applied papers. Also in the area of Numerical Analysis and
Computation we will find papers on numerical conformal mappings.
In Real Analysis we find papers on the central limit theorem, oscilla
tory integrals, wavelets, Brownian intersection measures, Caratheodory
convergence, iterative function systems, distribution theory, Minkowski
viii
inequalities, operator algebras, Fourier hyperfunctions, Stieltjes mo
ments, Whitney jets, Fatou sets, fractional powers of operators, ultra
distributions, etc. .
In the Applications and Differential Equations we have Hamilto
nian theory, the Fredholm determinant, wavelet analysis, Schwarzschild
space-time, singular integral operators, eigenvalue problems, quadra
ture formulae for hypersingular integrals, remote sensing, plasticity,
sound synthesis, Navier Stokes equations, nonlinear parabolic equa
tions, SchrOdinger equations, Sobolev spaces, wave propagation, gauge
invariant equations.
The subarea of FUnction Theoretic methods in differential equations
was also represented with papers on Clifford analysis,Cauchy singular
integrals, hyperanalytic boundary value problems, monogenic functions,
oblique derivative problems, etc.
The main responsibility of collecting and evaluating the contribu
tions to these volumes was taken by the session organizers. They had
organized the following sessions:
Value Distribution Theory and Complex Dynamics (P.C. Hu, X.H. Hua,
C.C. Yang),
Nevanlinna Theory and Related Topics (S. Mori),
Riemann Surfaces (Y. Imayoshi, H. Sato, H. Shiga),
8-Equations on Complex Manifolds (T. Ohsawa),
FUnction Space Theory in Complex Ball and Related Topics (E.G.
Kwon) ,
Infinite Dimeilsional Holomorphy (S. Dineen),
Complex Dynamics of Higher Dimension (M. Suzuki),
Complex and Funtional Analytic Methods in Partial Differential Equa-
tions (H. Begehr),
Integral Equations and Boundary Value Problems (G.-C. Wen),
Analytic Extension Formulas and their Applications (S. Saitoh),
Complex arid Numerical Analysis (J. Kajiwara),
Analytic FUnctionals, Hyperfunctions, and Generalized FUnctions (M.
Morimoto),
Constructive Methods in Applied Problems (P. Krutitskii),
Special Session (M. Reissig),
Potential Theory (P. Tamrazov),
FUnctional Analysis (A. Inoue),
ix
Spectral Theory of Differential Operators and Applications (B. Yain-
berg, S. Molchanov),
Function Spaces and Applications (Y. Burenkov, S. Samko),
Ocean Acoustics (R.P. Gilbert, G. Makrakis),
Inverse Problem in Acoustics (R.P. Gilbert, Y. Xu),
Direct and Inverse Scattering in Extended Inhomogeneous Environ
ments (L. Fishman),
Computational Biology (K. Harimoto),
Curve Theory and its Applications to Coding Theory (T. Kato).
Contributions in the same session adjoin each other in order of re
ception in this book .
The main work of composing the material to these two volumes were
achieved by the last named editor. It was also he who has managed to
get financial support for printing these volumes. We are grateful to •
the Commemorative Association for their Grant No. 11-56:
The Mathematical Society of Japan consented to support the Second
ISAAC Congress 7th April 1998. The Fukuoka Institute of Thchnology
acknowledged to hold the congress at FIT and consented to support the
congress 21st October 1998. Consequently, we could freely use confer
ence rooms, lecture rooms equipped with airconditioners and school bus
between FIT and Sasaguri, where participants from emerging countries,
i. e. from present and former socialist countries, countries under the
support of IMF and developing countries, stayed at the hotel said later.
The moral support of MSJ and the substantial support of FIT made
way for the local organizing committee to acquire the support of the
said Grant No. 11-56 from. 17th June 1999. The Grant No. 11-56
from • the Commemorative Association supported partially air fares
and fully the expenses necessary for the hotel at Sasaguri said later, of
all participants from the emerging countries.
The congress is also supported by Fukuoka Prefecture, Educational
Committee of Fukuoka Prefecture, Convention Bureau of Fukuoka City
and the Association for the Japan National Authorized Mathematics
Certification. By the support of the Educational Committee of Fukuoka
Prefecture, participants from the emerging countries got lodgings at the
