Related papers: Norms of polynomials of the Volterra operator
In this expository note, we compute the exact value of the norm of the resolvent of the Volterra operator.
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.
Conditions guaranteeing convergence of linear stochastic Volterra operators are studied. Necessary and sufficient conditions for mean square convergence are established, while almost sure convergence of the linear operator is shown to imply…
We derive a normal ordering formula for the operator \((xI)^n\), where \(I\) denotes the Volterra operator. The resulting coefficients are shown to coincide with the Bessel numbers. We also present two applications, along with a…
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.
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…
A method is presented for using coherent vectors to calculate the explicit form of Schur polynomials which are the coefficients of Laurent expansion of a vertex operator.
We study linear operators preserving the property of being a volume polynomial. More, precisely we show that a linear operator preserves this property if the associated symbol is itself a volume polynomial. This can be seen as an analogue…
We study the computability of the operator norm of a matrix with respect to norms induced by linear operators. Our findings reveal that this problem can be solved exactly in polynomial time in certain situations, and we discuss how it can…
We develop a unified framework for constructing matrix approximations to the convolution operator of Volterra type defined by functions that are approximated using classical orthogonal polynomials on $[-1, 1]$. The numerically stable…
We present two ways to compute the norm of a Foguel operator. One of these is algebraic and the other makes use of the Schur complement. This gives a two simpler proof of a result of Garcia. We also provide an extension of these results.
In the present paper we introduce a notion of homotopy of two Volterra operators which is related to fixed points of such operators. It is establish a criterion when two Volterra operators are homotopic, as a consequence we obtain that the…
Some results about existence, uniqueness, and attractive behaviour of solutions for nonlinear Volterra integral equations with non-convolution kernels are presented in this paper. These results are based on similar ones about nonlinear…
We introduce a notion of $\ell$-Volterra quadratic stochastic operator defined on $(m-1)$-dimensional simplex, where $\ell\in\{0,1,...,m\}$. The $\ell$-Volterra operator is a Volterra operator iff $\ell=m$. We study structure of the set of…
We give a new operator formula for Grothendieck polynomials that generalizes Magyar's Demazure operator formula for Schubert polynomials. Our proofs are purely combinatorial, contrasting with the geometric and representation theoretic tools…
~In this paper, we investigate the boundedness of some Volterra-type operators between ~$Zygmund$~ type spaces. Then, we give the essential norms of such operators in terms of ~$g,\varphi$, their derivatives and the n-th power ~$\varphi^n$…
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…
The dominant method for defining multivariate operator means is to express them as fix-points under a contraction with respect to the Thompson metric. Although this method is powerful, it crucially depends on monotonicity. We are developing…
Conditions for linear integral operators on $L_p$ over measure spaces to satisfy the polynomial covariance type commutation relations are described in terms of defining kernels of the corresponding integral operators. Representation by…
The sufficient conditions for existence and uniqueness of continuous solutions of the Volterra operator equations of the first kind with piecewise continuous kernel are derived. The asymptotic approximation of the parametric family of…