The usual expression for the secondary characteristical classes is regu-larized so that it ts for the case of Hilbert bundles. This gives index formulas for pseudodiierential operators with operator-valued symbols.

The main goal of this paper is to estimate the Hölder norm of a fractal version of the Hilbert transform in the Douglis analysis context acting from Hölder spaces of Douglis algebra valued functions defined on h-summable curves.

New special types of stationary conservative impedance and scattering systems, the so-called non-canonical systems, involving triplets of Hilbert spaces and projection operators, are considered. It is established that every matrix-valued Herglotz-Nevanlinna function of the form

Some new reverses of the Cauchy-Bunyakovsky-Schwarz integral inequality for vector-valued functions in Hilbert spaces that complement the recent results obtained in [1] are given. Applications for the Heisenberg inequality are provided.

We investigate the probabilistic and analytic properties of Volterra processes constructed as pathwise integrals deterministic kernels with respect to Holder continuous trajectories Hilbert-valued Gaussian processes. To this end, we extend sewing lemma from [18] two dimensional case, in order construct operator-valued Young type. prove that covariance operator associated infinite can be represe...