Regularity properties significantly stronger than were previously known are developed for four-dimensional non-linear conformally invariant quantized fields. The Fourier coefficients of the interaction Lagrangian in the interaction representation-i.e., evaluated after substitution of the associated quantized free field-is a densely defined operator on the associated free field Hilbert space K. ...

In this paper, in an arbitrary Hilbert space nonlocal boundary value problem for the Schrödinger equation with time dependent self-adjoint operator is studied. Stability estimates solution of established. To find approximate first order accuracy Rothe difference scheme and second Crank-Nicholson are constructed. these schemes have been obtained. obtain stability estimates, theory spectral repre...

In this paper, we design some iterative schemes for solving operator equation $ Lu=f $, where $ L:Hrightarrow H $ is a bounded, invertible and self-adjoint operator on a separable Hilbert space $ H $. In this concern,  Richardson and Chebyshev iterative methods are two outstanding as well as long-standing ones. They can be implemented in different ways via different concepts.In this paper...

The problem of computing linear force-free magnetic fields on a knotted multiply-connected domain is considered. The domain is the support of the current distribution, and the linear force-free fieldproblem reduces to finding an eigenfield of a self-adjoint curl operator. In this context, the GKN Theorem is reformulated in terms of symplectic geometry in order to characterize the self-adjoint e...

The article is devoted to building various dilatations of linear operators. explicit construction a unitary dilation compression operator considered. Then the J-unitary dilatation bounded constructed by means knot concept operator. Using Pavlov method, we construct self-adjoint dissipative We consider spectral and translational representations densely defined with nonempty set regular points. a...