Petkova, V.
Multipliers on a Hilbert space of functions on R
(pp. 207-216)
A B S T R A C T S
ON QUASI-NORMALITY OF TWO-SIDED MULTIPLICATION
M. Amouch
m.amouch@ucam.ac.ma
2000 Mathematics Subject Classification:
47B47, 47B10, 47A30.
Key words:
Bi-Multiplication, quasi-normalité,
spectraloide.
In this note, we characterize quasi-normality of two-sided
multiplication, restricted to a norm ideal and we extend this
result, to an important class which contains all quasi-normal
operators. Also we give some applications of this result.
BAYESIAN PREDICTION OF WEIBULL DISTRIBUTION BASED ON FIXED AND RANDOM SAMPLE SIZE
A. H. Abd Ellah
ahmhamed@hotmail.com
2000 Mathematics Subject Classification:
62E16, 65C05, 65C20.
Key words:
Predictive function, random sample size, predictive intervals,
Bayesian prediction.
We consider the problem of predictive interval for future
observations from Weibull distribution. We consider two cases
they are: (i) fixed sample size (FSS), (ii) random sample size
(RSS). Further, we derive the predictive function for both
FSS and RSS in closed forms. Next, the upper and lower
1%, 2.5%, 5% and 10% critical points for the predictive functions are calculated. To
show the usefulness of our results, we present some simulation
examples. Finally, we apply our results to some real data set in
life testing given in Lawless [16].
DENSITY OF POLYNOMIALS IN THE L^{2}
SPACE ON THE REAL AND THE IMAGINARY AXES AND IN A SOBOLEV SPACE
Lutz Klotz,
Sergey M. Zagorodnyuk
Sergey.M.Zagorodnyuk@univer.kharkov.ua
2000 Mathematics Subject Classification:
41A10, 30E10, 41A65.
Key words:
Density of polynomials, moment problem, measure.
In this paper we consider an L^{2} type space of scalar functions
L^{2}_{M, A} (RÈi R) which can be, in particular, the usual
L^{2} space of scalar functions on RÈiR. We find conditions
for density of polynomials in this space using a connection with the
L^{2} space of square-integrable matrix-valued functions on \mathbbR
with respect to a non-negative Hermitian matrix measure. The
completness of L^{2}_{M, A} (RÈi R ) is also established.
RELATIONSHIP BETWEEN EXTREMAL AND SUM PROCESSES GENERATED BY THE SAME POINT PROCESS
E. Pancheva
pancheva@math.bas.bg,
I. Mitov
ivan.mitov@finanalytica.com,
Z. Volkovich
vlvolkov@ort.org.il
2000 Mathematics Subject Classification:
Primary 60G51, secondary 60G70, 60F17.
Key words:
Extremal processes,
Increasing processes with independent increments, weak limit
theorems, Levy measure, Poisson point processes, Bernoulli point
processes, random sample size.
We discuss weak limit theorems for a uniformly
negligible triangular array (u.n.t.a.) in Z = [0,¥)×[0,¥)^{d}
as well as for the associated with it sum and extremal processes on
an open subset S. The complement of S turns out to be the
explosion area of the limit Poisson point process. In order to
prove our criterion for weak convergence of
the sum processes we introduce and study sum processes over
explosion area. Finally we generalize the model of u.n.t.a. to
random sample size processes.
COURBURE ET POLYGONE DE NEWTON
M. Hannachi
M_Hannachi@yahoo.fr,
K. Mezaghcha
khelifa.Mezaghcha@UHA.fr
2000 Mathematics Subject Classification:
26E35, 14H05, 14H20.
Key words:
Algebraic curve, curvature, non standard analysis.
The object of this article relates to the study of the complex algebraic
curves by using the concept of envelope convex. One proposes to characterize
the points of a holomorphic complex curve (C) and to associate a metric
invariant to them ( generalized curvature), by using the equations of the
various segments constituting the polygon of Newton associated with (C).
MULTIPLIERS ON A HILBERT SPACE OF FUNCTIONS ON R
Violeta Petkova
petkova@univ-metz.fr
2000 Mathematics Subject Classification:
42A45.
Key words:
Multipliers, spectrum.
For a Hilbert space H Ì L^{1}_{loc} (R) of functions on R we obtain a representation theorem for the multipliers M commuting with the shift operator S. This generalizes the classical result
for multipliers in L^{2}(R) as well as our previous result for multipliers in weighted space L^{2}_{w}(R). Moreover, we obtain a description of the spectrum of S.
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