ABSTRACT. With S a linearly ordered set with the least upper bound property, with g a nonincreasing real-valued function on S, and with A a densely denned dissipative linear operator, an evolution system M is developed to solve the modified Stieljes integral equation M(s, i)x = x + A((L)[sdgM(-, t)x). An affine version of this equation is also considered. Under the hypothesis that the evolufion...

We investigate the properties of the collision operator Q associated to the linear Boltzmann equation for dissipative hard-spheres arising in granular gas dynamics. We establish that, as in the case of non–dissipative interactions, the gain collision operator is an integral operator whose kernel is made explicit. One deduces from this result a complete picture of the spectrum of Q in an Hilbert...

In this work, an iterative method based on a matrix form of LSQR algorithm is constructed for solving the linear operator equation A(X) = B and the minimum Frobenius norm residual problem ||A(X)−B||F where X ∈ S := {X ∈ Rn×n | X = G(X)}, F is the linear operator from Rn×n onto Rr×s, G is a linear selfconjugate involution operator and B ∈ Rr×s. Numerical examples are given to verify the efficien...

We are concerned with some unbounded linear operators on the so-called p-adic Hilbert space Eω. Both the Closedness and the selfadjointness of those unbounded linear operators are investigated. As applications, we shall consider the diagonal operator on Eω, and the solvability of the equation Au = v where A is a linear operator on Eω. AMS subject classification. 47S10; 46S10; 47A05; 47B25.

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

We consider the problem of fitting a linear operator induced equation to point sampled data. In order to do so we systematically exploit the duality between minimizing a regularization functional derived from an operator and kernel regression methods. Standard machine learning model selection algorithms can then be interpreted as a search of the equation best fitting given data points. For many...

We approximate the solution of initial boundary value problems for equations of the form Au′(t) = B(t, u(t)), t ∈ [0, t?]. A is a linear, selfadjoint, positive definite operator on a Hilbert space (H, (·, ·)) and B is a possibly nonlinear operator. We discretize in space by finite element methods and for the time discretization we use explicit linear multistep schemes. We derive optimal order e...

In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...