Issue 1, Volume 23, June 1998

1998 · Open access

1. NONLINEAR MONOTONE ILL-POSED PROBLEMS IN BANACH SPACES NGUYEN BUONG PDF

   ▸ Abstract

   In this paper, convergence rates for an operator version of Tikhonov regularization constructing on the base of subdifferential of uniformly convex functional on real reflexive Banach space are obtained without both closeness conditions and parameter selection method. Then, the obtained results are considered in combination with finite-dimensional approximations of the space. An example is given for the illustration.

   3-12
2. DIFFERENTIABLE FUNCTIONS AND THE GENERATORS ON A HILBERT-LIE GROUP ERDAL COSKUN PDF

   ▸ Abstract

   A convolution semigroup plays an important role in the theory of probability measure on Lie groups. The basic problem is that one wants to express a semigroup as a Lévy-Khinchine formula. If $(\mu_t)_{t\in\mathbf{R}_+^*}$ is a continuous semigroup of probability measures on a Hilbert-Lie group $G,$ then we define
   $$T_{\mu_t}f:=\int f_a\mu_t(da)\quad (f\in C_*(G); \ t > 0).$$
   It is apparent that $(T_{\mu_t})_{t\in\mathbf{R}_+^*}$ is a continuous operator semigroup on the space $C_*(G)$ with the infinitesimal generator $N$. The generating functional $A$ of this semigroup is defined by $Af := \lim_{t\downarrow 0}\frac 1t (T_{\mu_t}f(e)-f(e))$. We consider the problem of construction of a subspace $C_{(2)}(G)$ of $C_*(G)$ such that the generating functional $A$ on $C_{(2)}(G)$ exists. This result will be used later to show that Lvy-Khinchine formula holds for Hilbert-Lie groups.

   13-24
3. EXISTENCE OF PERIODIC SOLUTIONS OF NONAUTONOMOUS RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS E. AIT DADS, K. EZZINBI PDF

   ▸ Abstract

   This paper is concerned with non-linear functional differential equations of retarded type which are periodic in the independent variable $t$. The aim is to obtain explicit conditions which are sufficient for the existence of periodic solutions if there exists a bounded solution.

   25-34
4. ON THE ALMOST PERIODIC $n$-COMPETING SPECIES PROBLEM TRINH TUAN ANH PDF

   ▸ Abstract

   We consider the $n$-dimensional Lotka-Volterra competition equations with almost periodic coefficients. Conditions for the existence of a globally asymptotically stable almost periodic solution with positive components are given. This is a generalization of a result in [5].

   35-48
5. SPECTRAL ANALYSIS OF SET-VALUED MAPPINGS ALBERTO SEEGER PDF

   ▸ Abstract

   This note deals with the spectral analysis of a general set-valued mapping $A$ defined from a normed space $X$ into its topological dual space $X^*$. The following two issues are addressed: (i) identification of set-valued mappings which have only nonnegative eigenvalues; (ii) analysis of recession eigenvalues and recession eigenvectors.

   49-63
6. REGULARIZED SOLUTIONS OF A CAUCHY PROBLEM FOR THE LAPLACE EQUATION IN AN IRREGULAR LAYER: A THREE DIMENSIONAL MODEL DANG DINH ANG, NGUYEN HOI NGHIA, NGUYEN CONG TAM PDF

   65-74
7. FINITE PROPER HOLOMORPHIC SURJECTIONS AND LINEAR TOPOLOGICAL INVARIANTS $(­\overline{\Omega})$ AND $(\widetilde{\Omega})$ DINH HUY HOANG PDF

   ▸ Abstract

   It is shown that linear topological properties $(­\overline{\Omega})$, $(\widetilde{\Omega})$ and isomorphisms of spaces of holomorphic functions are invariant under finite proper holomorphic surjections between Stein spaces.

   75-82
8. CRITICAL SOBOLEV EXPONENT FOR DEGENERATE ELLIPTIC OPERATORS NGUYEN MINH TRI PDF

   ▸ Abstract

   Semilinear equations for degenerate elliptic operators are considered. A simple proof of imbedding theorems for appropriate Sobolev spaces are given. Via generalized Pokhozaev identity we prove some nonexistence theorems for the equations.

   83-94
9. RELATION BETWEEN THE SPECTRUM OF OPERATORS AND LYAPUNOV EXPONENTS NGUYEN HUU DU, PHAN LE NA PDF

   ▸ Abstract

   The article concerned with the problem of regarding Lyapunov exponents of a random difference equation as the spectrum of an operator acting on a suitable space. Let $L$ be the set of all sequences of random variables having finite $p^{th}$ moments for some $p$ small, endowed with a certain topology. From the difference equation $X(n+1)=A(n)X(n)$; $X(0)=x\in R^d$, where $(A(n), \ n\in Z)$ is an i.i.d. sequence of random variables, we construct an operator $T$ acting on the space $L$. It is proved that the spectrum of the operator $T$ is contained in the set of sample Lyapunov exponents of this random dynamical system.

   95-106
10. CONVEX VECTOR FUNCTIONS AND THEIR SUBDIFFERENTIAL DINH THE LUC, NGUYEN XUAN TAN, PHAN NHAT TINH PDF

    ▸ Abstract

    The continuity of a convex vector function on relative interior points of its domain is studied. As a corollary of this we can see that a convex vector function is Lipschitz near any relative interior point of its domain. A new concept of subdifferential of a convex function is introduced and some its properties similar to those in the scalar case are shown. The inclusive relations between generalized Jacobian and subdifferential, the convexcity of a vector function and the monotonicity of its subdifferential are also established. Further, some neccessary and sufficient conditions for the existence of efficient solutions of vector optimization problems are also proved.

    107-127
11. SOME REMARKS ON RANDOM SERIES IN BANACH SPACES MARÍA JESÚS CHASCO, NGUYEN DUY TIEN, V. I. TARIELADZE PDF

    ▸ Abstract

    The aim of this note is to give: 1) a characterization of Banach spaces of cotype 2; 2) an example related to Rademacher series in the Schatten classes; 3) a characterization of finite dimensional Banach spaces.

    129-141
12. P-ADIC HYPERBOLICITY OF THE COMPLEMENT OF HYPERPLANES IN $P^n(C_p)$ NGUYEN THANH QUANG PDF

    ▸ Abstract

    An algorithm in terms of linear algebra to determine the Brody hyperbolicity of $P^n(C_p)-|\mathcal H|$ is given, where $\mathcal H$ is a set of hyperplanes in $P^n(C_p)$ which are not necessary in general position.

    143-149
13. ON GRÄTZER'S PROBLEM NGUYEN DUC DAT PDF

    151-160
14. WIDTH OF COMPLEXES OF MODULES SIAMAK YASSEMI PDF

    ▸ Abstract

    The concept of the width of complex of modules (that is a dual of depth) is introduced and the dual of the generalization of the Auslander-Buchsbaum equality is proved.

    161-169
15. SPECTRAL CRITERIA OF ABSTRACT FUNCTIONS; INTEGRAL AND DIFFERENCE PROBLEMS ALAA E. HAMZA, GILBERT L. MURAZ PDF

    ▸ Abstract

    Let $X$ be a complex Banach space and let $M$ be a closed subspace of $L^{\infty}(J,X)$, where $J\in \{\mathbf{R},\mathbf{R}^+\}$. We answer the following question: Under what conditions $\phi_s-\phi\in M \ \forall s\in J$ implies that $\phi\in M$. Some conditions will be imposed on $M$ to obtain the main result concerning the indefinite integral. These conditions guarantee the following implication: $F\in E(J,X)\Longrightarrow F\in M$, where $F$ is the integral $\int_0^t f(s)ds$ of $f\in M\cap C_{ub}(J,X)$. Also, we generalize Loomis' Theorem for almost periodic functions [19, Theorem 5], to a more general class of functions $M\subseteq L^{\infty}(\mathbf{R},X)$ containing $AP(\mathbf{R},X)$. The main result of Part IV is: If $\phi$ is uniformly continuous, bounded, such that the $M$-spectrum $\sigma_M(\phi)$ of $\phi$ is at most countable and, for every $\lambda\in\sigma_M(\phi)$, the function $e^{-i\lambda t}\phi(t)$ is ergodic, then $\phi\in M$.

    171-184