Related papers: Asymptotic behaviour of iterates of Volterra opera…
In the present paper, firstly, we consider the Volterra integral equation of second type for a remainder term in an asymptotic formula of an arithmetic function which satisfies some special conditions and obtained a solution of the…
Bounded linear operators on separable Banach spaces algebraically similar to the classical Volterra operator $V$ acting on $C[0,1]$ are characterized. From this characterization it follows that $V$ does not determine the topology of…
It is shown that every operator on (C[0,1]) which preserves a copy of an asymptotic (\ell_1) space, also preserves a copy of (C[0,1]).
We consider $\ell$-Volterra quadratic stochastic operators defined on $(m-1)$-dimensional simplex, where $\ell\in\{0,1,...,m\}$. Under some conditions on coefficients of such operators we describe Lyapunov functions and apply them to obtain…
Let S be the multiplication operator by an independent variable x in L_2(0,1) and V be an integral operator of Volterra type. We find conditions for T:=S+V to be similar to S and discuss some generalisations of the results obtained to an…
In the present paper we consider a family of non-Volterra quadratic stochastic operators depending on a parameter $\alpha$ and study their trajectory behaviors. We find all fixed points for a non-Volterra quadratic stochastic operator on a…
In this paper we study the asymptotic behavior of second-order uniformly elliptic operators on weighted Riemannian manifolds. They naturally emerge when studying spectral properties of the Laplace-Beltrami operator on families of manifolds…
We study multidimensional stochastic volatility models in which the volatility process is a positive continuous function of a continuous multidimensional Volterra process that can be not self-similar. The main results obtained in this paper…
In general there exists no relationship between the fixed point sets of the composition and of the average of a family of nonexpansive operators in Hilbert spaces. In this paper, we establish an asymptotic principle connecting the cycles…
This thesis is devoted to asymptotic norm estimates for oscillatory integral operators acting on the L^2 space of functions of one real variable. The operators in question have compact support and an oscillatory kernel of the form exp(i…
In this paper we prove the well-posedness and we study the asymptotic behavior of nonoscillatory $L^p$-solutions for a third order nonlinear scalar differential equation. The equation consists of two parts: a linear third order with…
New asymptotic relations between the $L_p$-errors of best approximation of univariate functions by algebraic polynomials and entire functions of exponential type are obtained for $p\in (0,\iy]$. General asymptotic relations are applied to…
In this paper, we obtain asymptotic formulae on nilmanifolds $\Gamma \backslash G$, wher $G$ is any stratified (or even graded) nilpotent Lie group equipped with a co-compact discrete subgroup $\Gamma$. We study especially the asymptotics…
For Volterra operator $V\colon L^1(0,1) \to C[0,1]$ and summation operator $\sigma\colon \ell^1 \to c$, we obtain exact values of Approximation, Gelfand, Kolmogorov, Mityagin and Isomorphism numbers.
Using complex analysis techniques we obtain precise asymptotic approximations for the kernels corresponding to the symmetric $\alpha$-stable processes and their fractional derivatives. We apply our method to general L\'evy processes whose…
In this paper we present results on asymptotic characteristics of multivariate function classes in the uniform norm. Our main interest is the approximation of functions with mixed smoothness parameter not larger than $1/2$. Our focus will…
We determine the asymptotic behavior of the realized power variations, or more generally of sums of a given test function evaluated at the successive increments of a L\'{e}vy process. One can completely elucidate the first order behavior…
In the present paper, we are aiming to study limiting behavior of infinite dimensional Volterra operators. We introduce two classes $\tilde {\mathcal{V}}^+$ and $\tilde{\mathcal{V}}^-$of infinite dimensional Volterra operators. For…
We study the properties of the Volterra and Ces\`aro operators viewed on the $L^1$-M\"untz space $M_\Lambda^1$ with range in the space of continuous functions. These operators are neither compact nor weakly compact. We estimate how far from…
In the present paper, we study Lotka-Volterra (LV) type operators defined in finite dimensional simplex. We prove that any LV type operator is a surjection of the simplex. After, we introduce a new class of LV-type operators, called $M$LV…