Related papers: Spectral approximation of convolution operator
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…
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…
We develop a technique of proving standard estimates in the setting of Laguerre function expansions of convolution type, which works for all admissible type multi-indices $\alpha$ in this context. This generalizes a simpler method existing…
We determine the spectrum of the Voltterra-type integral operators $V_g$ on the growth type Fock--Sobolev spaces $\mathcal{F}_{\psi_m}^\infty$. We also characterized the bounded and compact spectral properties of the operators in terms of…
Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are…
We establish new explicit connections between classical (scalar) and matrix Gegenbauer polynomials, which result in new symmetries of the latter and further give access to several properties that have been out of reach before: generating…
Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the…
Operator monotone functions, introduced by Lowner in 1934, are an important class of real-valued functions. They arise naturally in matrix and operator theory and have various applications in other branches of mathematics and related…
We describe symmetric diffusion operators where the spectral decomposition is given through a family of orthogonal polynomials. In dimension one, this reduces to the case of Hermite, Laguerre and Jacobi polynomials. In higher dimension,…
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…
We consider a four-parameter family of non-Volterra operators defined on the two-dimensional simplex and show that, with one exception, each such operator has a unique fixed point. Depending on the parameters, we establish the type of this…
The numerical solution of dynamical systems with memory requires the efficient evaluation of Volterra integral operators in an evolutionary manner. After appropriate discretisation, the basic problem can be represented as a matrix-vector…
Sharp upper and lower estimates are obtained of the approximation numbers of a Sobolev embedding and an integral operator of Volterra type. These lead to asymptotic formulae for the approximation numbers and certain other s-numbers.
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…
We consider positive, integral-preserving linear operators acting on $L^1$ space, known as stochastic operators or Markov operators. We show that, on finite-dimensional spaces, any stochastic operator can be approximated by a sequence of…
A method for approximate solution of initial value and spectral problems for one dimensional Dirac equation based on an analytic approximation of the transmutation operator is presented. In fact the problem of numerical approximation of…
We study Jacobi operators $J_{p}$, $p> -1$, whose eigenfunctions are Laguerre polynomials. All operators $J_{p}$ have absolutely continuous simple spectra coinciding with the positive half-axis. This fact, however, by no means imply that…
This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of the arguments, a class we term ``spectral functions.'' We…
The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional…
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.