Iterated solutions of linear operator equations with the Tau method

Iterated solutions of linear operator equations with the Tau method

The Tau Method produces polynomial approximations of solutions of differential equations. The purpose of this paper is (i) to extend the recursive formulation of this method to general linear operator equations defined in a separable Hilbert space, and (ii) to develop an iterative refinement procedure which improves on the accuracy of Tau approximations. Applications to Fredholm integral equati...

Hypergeometric series solutions of linear operator equations

Hermitian solutions to the system of operator equations T_iX=U_i.

In this article we consider the system of operator equations T_iX=U_i for i=1,2,...,n and give necessary and suffcient conditions for the existence of common Hermitian solutions to this system of operator equations for arbitrary operators without the closedness condition. Also we study the Moore-penrose inverse of a ncross 1 block operator matrix and. then gi...

Index theory for linear self-adjoint operator equations and nontrivial solutions for asymptotically linear operator equations

We will first establish an index theory for linear self-adjoint operator equations. And then with the help of this index theory we will discuss existence and multiplicity of solutions for asymptotically linear operator equations by making use of the dual variational methods and Morse theory. Finally, some interesting examples concerning second order Hamiltonian systems, first order Hamiltonian ...

The solutions to some operator equations in Hilbert $C^*$-module

In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, we nd explicit solution of the operator equation $TXS^*-SX^*T^*= A$.