相关论文: On Dynamics of $\ell$- Volterra Quadratic Stochast…
We study some mapping properties of Volterra type integral operators and composition operators on model spaces. We also discuss and give out a couple of interesting open problems in model spaces where any possible solution of the problems…
Two necessary and sufficient conditions for an operator to be semi-normal are revealed. For a Volterra integration operator the set where the operator and its adjoint are metrically equal is described.
In this note, we mainly study operator-theoretic properties on Besov space $B_{1}$ on the unit disc. This space is the minimal Mobius invariant space. Firstly, we consider the boundedness of Volterra type operators. Secondly, we prove that…
In this paper we introduce a notion of $F-$ quadratic stochastic operator. For a wide class of such operators we show that each operator of the class has unique fixed point. Also we prove that any trajectory of the $F$-quadratic stochastic…
We study the real and imaginary parts of the powers of the Volterra operator on $L^2[0,1]$, specifically their eigenvalues, their norms and their numerical ranges.
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.
In this paper we study Volterra type operators on infinite dimensional simplex. It is provided a sufficient condition for Volterra type operators to be bijective. Furthermore it is shoved that the condition is not necessary.
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. The general problem in the nonlinear…
We study the class of continuous polynomial Volterra processes, which we define as solutions to stochastic Volterra equations driven by a continuous semimartingale with affine drift and quadratic diffusion matrix in the state of the…
We investigate the geometric properties of the Volterra-type integral operator \begin{equation*} T_g[f](z) = \int_{0}^{z} f(s)\, g'(s)\, ds, \quad |z|<1, \end{equation*} acting on various subclasses of analytic functions in the unit disk.…
In this paper, we introduce Volterra evolution algebras which are evolution algebras whose structural matrices are described by skew symmetric matrices. A main result of the present paper gives a connection between such kind of algebras…
Let $\omega$ be an unbounded radial weight on $\mathbb{C}^d$, $d\ge 1$. Using results related to approximation of $\omega$ by entire maps, we investigate Volterra type and weighted composition operators defined on the growth space…
The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Pel\'{a}ez, who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces. However, their characterizations for…
The algebraic study of special integral operators led to the notions of Rota-Baxter operators and shuffle products which have found broad applications. This paper carries out an algebraic study of general integral operators and equations,…
We study classical solutions (existence, uniqueness, and explicit solution operator) for homogeneous, linear, and semilinear abstract Volterra integral equations of wave type with almost sectorial operators. We use a functional calculus for…
In this paper we give complete descriptions of the set of square roots of certain classical operators, often providing specific formulas. The classical operators included in this discussion are the square of the unilateral shift, the…
We derive asymptotic information on the iterates of a Volterra convolution operator acting on L^p(0,1), subject to a mild smoothness condition on the kernel. In particular, an asymptotically equal sequence of rank 1 operators is obtained,…
We examine two nonselfadjoint operator algebras: the weighted shift algebra, and the Volterra operator algebra. In both cases, the operator algebra is the norm closure of the polynomials in the operator norm. In the case of the weighted…
We examine the multiple Hamiltonian structure and construct a symplectic realization of the Volterra model. We rediscover the hierarchy of invariants, Poisson brackets and master symmetries via the use of a recursion operator. The rational…
In this work, we consider the regularity property of stochastic convolutions for a class of abstract linear stochastic retarded functional differential equations with unbounded operator coefficients. We first establish some useful estimates…