Dynamical systems method (DSM) for selfadjoint operators

Iterative solution of linear equations with unbounded operators

A convergent iterative process is constructed for solving any solvable linear equation in a Hilbert space, including equations with unbounded, closed, densely defined linear operators. The method is proved to be stable towards small perturbation of the data. Some abstract results are established and used in an analysis of variational regularization method for equations with unbounded linear ope...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Selfadjoint time operators and invariant subspaces

For classical dynamical systems time operators are introduced as selfadjoint operators satisfying the so called weak Weyl relation (WWR) with the unitary groups of time evolution. Dynamical systems with time operators are intrinsically irreversible because they admit Lyapounov operators as functions of the time operator. For quantum systems selfadjoint time operators are defined in the same way...

1 2 Ja n 20 06 DSM for solving ill - conditioned linear algebraic systems ∗ †

A standard way to solve linear algebraic systems Au = f, (*) with ill-conditioned matrices A is to use variational regularization. This leads to solving the equation (A * A + aI)u = A * f δ , where a is a regularization parameter, and f δ are noisy data, ||f − f δ || ≤ δ. Numerically it requires to calculate products of matrices A * A and inversion of the matrix A * A + aI which is also ill-con...

Error bounds in approximating n-time differentiable functions of self-adjoint operators in Hilbert spaces via a Taylor's type expansion

On utilizing the spectral representation of selfadjoint operators in Hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in Hilbert Spaces via a Taylor's type expansion are given.