Abidi, J.
Contribution à l'étude des fonctions plurisousharmoniques
convexes et analytiques
(pp. 329−388)
A B S T R A C T S
SUBORDINATED MARKOV BRANCHING PROCESSES AND LÉVY PROCESSES
Penka Mayster
penka.mayster@abv.bg
2010 Mathematics Subject Classification:
60J80, 60K05.
Key words:
subordinated Lévy processes,
Poisson random measure, pure jump Markov processes, Kolmogorov
backward equation.
We consider the jump structure of the subordinated Lévy
processes and subordinated Markov branching processes. Subordination
provides a method of constructing a large subclass of Markov or
Lévy processes Y(t) = X(T(t)), where X(t) is a Markov or
Lévy process and T(t) is a continuous time subordinator
independent of X(t); that is a Lévy process with positive
increments and T(0) = 0. Let X(t) be a Lévy process. Then
subordination preserves the independence and stationarity of the
increments, but it changes their amplitudes and the total mass of
the Lévy measure. Let X(t) be a Markov branching process. Then
subordination (owing to the independence of X(t) and T(t))
preserves the Markov property, but it disturbs the branching
property. The infinitesimal generator of the subordinated process
$(t) involves the total progeny of reproduction. The intensity of
the jump times depends on the subordinator's Bernstein function.
ON LIE ALGEBRAS WITH EXPONENTIAL GROWTH OF THE CODIMENSIONS
O. A. Bogdanchuk
bogdanchuk_o_a@mail.ru,
S. P. Mishchenko
mishchenkosp@mail.ru,
A. B. Verëvkin
abverevkin@gmail.com
2010 Mathematics Subject Classification:
17B01, 16R10, 16P90.
Key words:
variety of Lie algebras, polynomial identity, codimension sequence, exponent of variety.
We study the asymptotic behaviour of the codimension sequence of varieties of Lie algebras variety over a field of characteristic zero. We construct an infinite series of such varieties with different fractional exponents. This extends the special cases known before.
ESSENTIAL NORMS OF WEIGHTED COMPOSITION OPERATORS ON L^{1} MÜNTZ SPACES
Ihab Al Alam
ihabalam@yahoo.fr,
Pascal Lefèvre
pascal.lefevre@univ-artois.fr
2010 Mathematics Subject Classification:
47B33, 47B38.
Key words:
Müntz spaces, compact operators, composition operators,
essential norm.
This paper discusses the problem of boundedness and compactness for weighted composition operators defined on a Müntz subspace of L^{1}([0, 1]). We compute the essential norm of such operators when the symbol φ of the composition operator satisfies a special condition (condition (B)). As a corollary, we obtain the exact values of essential norms of composition and multiplication operators. This completes the corresponding results of the first named author in the framework of Müntz subspaces of C([0, 1]).
EMPIRICAL BAYES TWO-SIDED TEST FOR THE PARAMETER
OF LINEAR EXPONENTIAL DISTRIBUTION FOR RANDOM INDEX
Huang Juan
huangjuan401178@163.com
2010 Mathematics Subject Classification:
62C12, 62F15.
Key words:
random index, empirical Bayes test, asymptotic optimality, convergence rates.
In the case of random index, the empirical Bayes two-side test rule for the parameter of linear exponential distribution is constructed. The asymptotically optimal property for the proposed EB test is obtained under suitable conditions. It is shown that the convergence rates of the proposed EB test rules can arbitrarily close to O(n^{−½}).
STRONG CONVERSE RESULT FOR BASKAKOV OPERATOR
Ivan Gadjev
gadjevivan@hotmail.com
2010 Mathematics Subject Classification:
41A36, 41A25, 41A27, 41A17.
Key words:
Baskakov operator, K-functional, Strong converse inequality.
We give a strong converse inequality of type A in terms of K-functional K_{ψ}(f,t) for classical Baskakov operator.
In order to establish it, we use the iterated Baskakov operator and, in particular, we prove the Voronovskaya and Bernstein-type inequalities for it.
NOTES ON LATTICE ORDERED ALGEBRAS
Rusen Yιlmaz
ryilmaz00@yahoo.com
2010 Mathematics Subject Classification:
Primary 46A40, 46B42; Secondary 06F25, 13J25.
Key words:
lattice ordered algebra, Riesz algebra, f-algebra, almost f-algebra, d-algebra, pseudo-almost f-algebra.
In this paper we introduce a new class of lattice ordered algebra, which will be called a pseudo-almost f-algebra; namely, a lattice ordered algebra A in which a ∧ b = 0 in A implies ab ∧ ba = 0. We present
some fundamental properties of pseudo-almost f-algebras and consider their
relationships with various type of lattice ordered algebras; mainely,
f-algebras, almost f-algebras and d-algebras.
CONTRIBUTION À L'ÉTUDE DES FONCTIONS PLURISOUSHARMONIQUES
CONVEXES ET ANALYTIQUES
Jamel Abidi
abidijamel1@gmail.com
2010 Mathematics Subject Classification:
32A10, 32A60, 32U05, 32U15, 32T05.
Key words:
Analytic convex and plurisubharmonic
functions, harmonic function, maximum principle.
We establish in this paper some new
relations between convex, plurisubharmonic and analytic functions in
C^{n}, n ≥ 1.
Let g: C^{n} → C be analytic. We prove that
{b ∈ C : |g + b| is a convex function in C^{n}} = ∅ or α or C,
where α ∈ C.
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