Prof. E. C. Titchmarsh, F.R.S.

Prof. Dr. Prof. Prof.

Generalizing the Titchmarsh Divisor Problem

Let a be a natural number different from 0. In 1963, Linnik proved the following unconditional result about the Titchmarsh divisor problem ∑ p≤x d(p− a) = cx + O ( x log log x log x ) where c is a constant dependent on a. Titchmarsh proved the above result assuming GRH for Dirichlet L-functions in 1931. We establish the following asymptotic relation: ∑ p≤x p≡a mod k d ( p− a k ) = Ckx + O ( x l...

Gutachter: Prof. Dr.-Ing. habil. Dr. h. c. Lothar Mörl

A two-dimensional balance model of populations distributed by property was developed using the ordinates of particle diameter andparticle density. This model makes it possible to calculate the spectrums of granulation changing over time in the fluidized bed duringbatch operation and in addition to calculate the time-dependent size distribution of the product granulate for continuous...

Elected FRS 1976

On Periodic Matrix-Valued Weyl-Titchmarsh Functions

We consider a certain class of Herglotz-Nevanlinna matrix-valued functions which can be realized as the Weyl-Titchmarsh matrix-valued function of some symmetric operator and its self-adjoint extension. New properties of Weyl -Titchmarsh matrixvalued functions as well as a new version of the functional model in such realizations are presented. In the case of periodic Herglotz-Nevanlinna matrix-v...