Serdica Mathematical Journal
Volume 32, Number 4, 2006
C O N T E N T S
Articles

Fabian, M., P. Hájek, V. Montesinos, V. Zizler.
Weakly compact generating and shrinking Markusevic bases
(pp. 277288)

Zolotarev, V. A., R. Hatamleh.
On connection between characterestic functions and the Caratheodori class functions
(pp. 289302)

Zapryanova, T.
A characterization theorem for the Kfunctional associated with the algebraic
version of trigonometric Jackson integrals
(pp. 303322)

Mokkadem, A., M. Pelletier, B. Thiam.
Large and moderate deviations principles for recursive kernel estimator of a
multivariate density and its partial derivatives
(pp. 323354)

Shaska, T.
Subvarieties of the hyperelliptic moduli determined by group actions
(pp. 355374)

Komeda, J., A. Ohbuci.
Corrigendum for "Weierstrass points with first nongap four on a
double covering of a hyperelliptic curve", Serdica Math. J.
30 (2004), 4354
(pp. 375378)
Book Reviews

Rusev, P. (Reviewer)
Selected Papers, I, II by Nikola Obrechkoff
(pp. 379382)

Kutev, N. (Reviewer)
Geometrical Methods for Solving of Fully
Nonlinear Partial Differential Equations by P. Popivanov
(pp. 383386)
A B S T R A C T S
WEAKLY COMPACT GENERATING AND SHRINKING MARKUSEVIC BASES
M. Fabian
fabian@math.cas.cz
P. Hájek
hajek@math.cas.cz
V. Montesinos
vmontesinos@mat.upv.es
V. Zizler
zizler@math.cas.cz
2000 Mathematics Subject Classification: 46B30, 46B03.
Key words:
Weakly compactly generated spaces, shrinking Markusevic bases,
Eberlein compacta.
It is shown that most of the well known classes of nonseparable
Banach spaces related to the weakly compact generating can be
characterized by elementary properties of the closure of the
coefficient space of Markusevic bases for such spaces. In some
cases, such property is then shared by all Markusevic bases in the
space.
ON CONNECTION BETWEEN CHARACTERESTIC FUNCTIONS AND THE
CARATHEODORI CLASS FUNCTIONS
Vladimir A. Zolotarev
Vladimir.A.Zolotarev@univer.kharkov.ua
Raéd Hatamleh
raedhat@yahoo.com
2000 Mathematics Subject Classification: 47A65, 45S78.
Key words:
Characterestic function, Caratheodori class function, colligation,
homographic transformation.
Connection of characteristic functions S(z) of nonunitary
operator T with the functions of Caratheodori class is
established. It was demonstrated that the representing measures from
integral representation of the function of Caratheodori's class are
defined by restrictions of spectral measures of unitary dilation, of
a restricted operator T on the corresponding defect subspaces.
A CHARACTERIZATION THEOREM FOR THE KFUNCTIONAL ASSOCIATED WITH THE
ALGEBRAIC VERSION OF TRIGONOMETRIC JACKSON INTEGRALS
T. Zapryanova
teodorazap@abv.bg
2000 Mathematics Subject Classification:
41A25, 41A36.
Key words:
KFunctional, Modulus of smoothness, Jackson integral.
The purpose of this paper is to present a characterization of a
certain Peetre Kfunctional in L_{p}[−1,1] norm, for
1 ≤ p ≤ 2 by means of a modulus of smoothness. This modulus is based
on the classical one taken on a certain linear transform of the
function.
LARGE AND MODERATE DEVIATIONS PRINCIPLES FOR RECURSIVE
KERNEL ESTIMATOR OF A MULTIVARIATE DENSITY AND ITS PARTIAL
DERIVATIVES
Abdelkader Mokkadem
mokkadem@math.uvsq.fr
Mariane Pelletier
pelletier@math.uvsq.fr
Baba Thiam
thiam@math.uvsq.fr
2000 Mathematics Subject Classification:
62G07, 60F10.
Key words:
Multivariate recursive kernel estimation of a density and its
derivatives; large and moderate deviations principles.
In this paper we prove large and moderate deviations principles for
the recursive kernel estimator of a probability density function and
its partial derivatives. Unlike the density estimator, the
derivatives estimators exhibit a quadratic behaviour not only for
the moderate deviations scale but also for the large deviations one.
We provide results both for the pointwise and the uniform
deviations.
SUBVARIETIES OF THE HYPERELLIPTIC MODULI DETERMINED BY
GROUP ACTIONS
T. Shaska
shaska@oakland.edu
2000 Mathematics Subject Classification:
14Q05, 14Q15, 14R20, 14D22.
Key words:
Hyperelliptic curves, automorphism groups.
Let H_{g} be the moduli space of genus g hyperelliptic
curves. In this note, we study the locus
H_{g} (G,σ) in H_{g} of curves admitting a Gaction of
given ramification type σ and inclusions between such loci. For
each genus we determine the list of all possible groups, the
inclusions among the loci, and the corresponding equations of the
generic curve in H_{g} (G, σ). The proof of the
results is based solely on representations of finite subgroups of
PGL_{2} (C) and the RiemannHurwitz formula.
CORRIGENDUM
for
WEIERSTRASS POINTS WITH FIRST NONGAP FOUR ON A
DOUBLE COVERING OF A HYPERELLIPTIC CURVE
Serdica Math. J. 30 (2004), 4354
Jiryo Komeda
komeda@gen.kanagawait.ac.jp
Akira Ohbuci
ohbuchi@ias.tokushimau.ac.jp
In the proof of Lemma 3.1 in [1] we need to show that we may take
the two points p and q with p ≠ q such that
p+q+(b2)g_{2}^{1}(C′)∼2(q_{1}+…
+q_{b1}) 

where q_{1},…,q_{b1} are points of C′, but in the paper
[1] we did not show that p ≠ q. Moreover, we hadn't been able to
prove this using the method of our paper [1]. So we must add some
more assumption to Lemma 3.1 and rewrite the statements of our paper
after Lemma 3.1. The following is the correct version of Lemma 3.1
in [1] with its proof.
P. Rusev (Reviewer)
NIKOLA OBRECHKOFF, SELECTED PAPERS, VOL I, II
Prof. Marin Drinov Academic Publishing House, 2006
vol I, XII + 361 pp., EURO 20, ISBN 10 9543221200(I), ISBN 13 9789543221202(I)
vol II, XIV + 474 pp., EURO 20, ISBN 10 9543221219(II), ISBN 13
9789543221219(II).
2000 Mathematics Subject Classification:
0002,00B60,01A75.
Key words:
Classical analysis, summation of
divergent series, Diophantine approximations, probability theory.
Contact information:
baspress@abv.bg
Nikolai Kutev
kutev@math.bas.bg (Reviewer)
GEOMETRICAL METHODS FOR SOLVING OF FULLY NONLINEAR PARTIAL
DIFFERENTIAL EQUATIONS,
by P. Popivanov
popivano@math.bas.bg,
Mathematics and its Applications Vol. 2,
Union of Bulgarian Mathematicians, Sofia,
2006,
X + 158 pp., EURO 49, ISBN 10 9548880245, ISBN 13 9789548880244
2000 Mathematics Subject Classification:
3502, 5302, 35B65, 35C05, 35F20, 35G25, 35L60, 57R45,
58C28, 76J05.
Key words:
Method of characteristics, MongeAmpere, eikonal,
Clairaut equations, propagation of singularities, anomalous and
generic singularities of the integral surfaces, semilinear
hyperbolic systems, Hamiltonian systems, canonical transformations.
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