Topics in analysis and its applications : proceedings of the NATO Advanced Research Workshop, Yerevan, Armenia, 22-25 September, 2002

484 Pages·2004·3.08 MB·English

by  Grigor A Barsegian

Topics in Analysis and its Applications
NATO Science Series
A Series presenting the results of scientific meetings supported under the NATO Science
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Series II:Mathematics,Physics and Chemistry – Vol.147
Topics in Analysis and its
Applications
edited by
G.A.Barsegian
Institute of Mathematics of National Academy of Sciences of Armenia,
Yerevan, Armenia
and
H.G.W.Begehr
Mathematical Institute,
Freie Universität Berlin,
Berlin, Germany
KLUWER ACADEMIC PUBLISHERS
NEW YORK,BOSTON, DORDRECHT, LONDON, MOSCOW
eBookISBN: 1-4020-2128-3
Print ISBN: 1-4020-2062-7
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Table of Contents
Preface ix
Shilov boundary for normed algebras 1
A. Escassut and N.M. Netti
BMO-mappings in the plane 11
C. Andreian Cazacu and V. Stanciu
Harmonic forms on non-orientable surfaces 31
A. Alonso, A. Fern´andez and J. P´erez
Periodic Fatou components and singularities of the inverse
function 47
W. Bergweiler
On the normality of topological target manifolds for Riemann-
Hilbert problems 61
E. Wegert and G. Semmler
Geometric aspects of generalized analytic functions 69
G. Giorgadze
The Riemann-Hilbert boundary value problem on a cut plane 83
N. Manjavidze
On the logarithmic derivative of meromorphic functions 91
A.A. Mokhon’ko and A.Z. Mokhon’ko
Methods for studying level sets of smooth enough functions 105
G.A. Barsegian and G.A. Sukiasyan
Gamma-lines of polynomials and a problem by Erdo¨s-Herzog-
Piranian 119
G.A. Barsegian
A method for studying oscillations of nonlinear differential equa-
tions. Applications to some equations in biology and economics 123
K. Barseghyan and G.A. Barsegian
vi
Counting points of semi-algebraic subsets 149
T. Aliashvili
Behaviour at infinity of polynomials of two variables 163
H.G. Ghazaryan and V.N. Margaryan
On some properties of degenerate elliptic systems of partial
differential equations 191
A. Dzhuraev
Formulas for derivatives of solutions of the ∂−equation in the
ball 229
A.I. Petrosyan
On some complex differential and singular integral operators 235
H. Begehr and A. Dzhuraev
Boundary and initial value problems for higher order PDEs in
Clifford analysis 271
E. Obolashvili
On unique solvability of the Dirichlet problem for one class of
properly elliptic equations 287
A.O. Babayan
Dirichlet problems with nonsmooth boundary 295
A.O. C¸elebi
Dirichlet problem in the half-plane for RO−varying weight
functions 311
H. Hairapetian
About one class of Volterra type linear integral equations with
an interior fixed singular or super-singular point 317
N. Rajabov
The method of discrete singularities of solutions of singular
integral equations with unmoved singularity 327
A. Sahakyan
Localization operators, Wigner transforms and paraproducts 333
M.W. Wong
The flight of an aircraft along a given trajectory and optimal
flight control 347
N.E. Tovmasyan
On mathematical problems of two-dimensional tomography 365
A. Vagarshakyan
vii
On a mixed problem for a composite plane weakened by
arc-type cracks 377
V.N. Hakobyan and L.L. Dashtoyan
Solution of the two-dimensional magnetoelastic Lamb problem 385
G.Y. Baghdasaryan, Z.N. Danoyan and M.A. Mikilyan
On an eigenvalue problem for the anisotropic strip 397
M. Aghalovyan
On singular perturbed equations of thin bodies 403
L. Aghalovyan
Exactly solvable models of stochastic quantum mechanics within
the framework of Langevin-Schro¨dinger type equations 415
A.S. Gevorkyan
Generating functions and wavelet-like decompositions 443
A. Nersessian
Index of Names 453
Index of Subjects 457
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Preface
Subsequent to an International ISAAC Conference on “Complex Anal-
ysis, Differential Equations and Related Topics”, the NATO ARW
Topics in Analysis and its Applications
took place in Yerevan, Armenia with participants from Armenia, Aus-
tria,Belarus,Canada,Finland,Georgia,Germany,Italy,Marocco,Poland,
Portugal, Romania, Russia, Spain, Sweden, Tajikistan, Turkey, Ukraine,
USA.Thepresentvolumereflectsthemaincontributionsbutneitherthe
stimulating atmosphere nor the highly friendly relations among the par-
ticipants. Thanks are due to many members of the family of Grigor
Barsegian, the Armenian co-director of this ARW. They have helped a
lottomakethefourdayspleasantandeasyforallparticipants. Without
the support from the Scientific and Environmental Affairs Devision of
the NATO the event would not have taken place. All participants were
very grateful to Dr. F. Pedrazzini, the Programme Director of Phys-
ical and Engineering Science and Technology and his staff for having
arranged the support in time although it was very tough before the be-
ginning.
Most topics in the workshop were devoted to complex analysis as well
of one as of several complex variables. Several contributions came from
elasticity theory.
Onegeneralizationofcomplexanalysisisthetheoryofp-adicanalysis,
a field enjoying a lot of attention in recent years. Multiplicative semi-
norms in an ultrametric normed algebra have many applications in the
study of analytic elements in p-adic analysis. Here the existence of
a Shilov boundary for a semi-multiplicative semi-norm defined on an
algebra is found inside a set of multiplicative semi-norms.
In geometric function theory quasiconformal mappings are studied a
lot since almost 80 years. This concept is called quasiregular in higher
dimensions. More recent research involves mappings of bounded mean
oscillations. Thisresearchissurveyedonaswellforplanedomainsasfor