Finally, for the solution of this problem, a priori estimate in the norm of space (C [0,T],L_{2}[0,l])) was obtained.
Nevertheless, for the solution of the difference scheme (10) the coercive stability estimate in the norm of same fractional spaces E α ( 0 < α < 1 ) under the supplementary restriction of the operator A is established.
We show that for functions f in the Besov class (B_{infty,1}^1({mathbb R}^2)) and for (pin [1,2]) we have a Lipschitz type estimate in the Schatten von Neumann norm ({varvec{S}}_p) for functions of pairs of noncommuting self-adjoint operators, but there is no such a Lipschitz type estimate in the norm of ({varvec{S}}_p) with (p>2) as well as in the operator norm.
In many applications it is desirable to be able to compute estimates of the norm of the error in the approximate solutions generated and terminate the iterations when the estimates are sufficiently small.
An alternative would be to generalize only the part of the results related to the exponential stability in the metric and the related estimates of the norms of solutions in the case of exponential stability and in the case of the exponential stability being not guaranteed (omitting the case of exponential stability in the metric and estimates of the norm of a derivative of solution).
The discrepancy principle requires that an estimate of the norm of the noise in the contaminated image be available.
However, in order to implement this algorithm, one has first to compute (or, at least, estimate) the norm of A, which is in general not an easy work in practice.
We proceed to estimate the norm of the term in the right-hand side.
In this section we list several results on estimates of the norms of (f(A -f B)) in operator ideals and, in particular, in Schatten von Neumann classes.
We find relations between the estimates of the norms of intermediate derivatives operators in the subspace W 2 3 ( R + ; H ) and the solvability conditions.
