Obviously the operators Ln are positive linear operators on the space of locally integrable functions on I of polynomial growth as t→∞, provided that n is sufficiently large. In 1995, Stancu [10] gave a derivation of these operators and investigated their approximation properties. We mention that similar operators arise in the work by Adell et al. [3, 4] by taking the probability density of the...

The standard way to obtain explicit formulas for spectral factorization problems for rational transfer functions is to use a minimal realization and then obtain formulae in terms of the generators A, B, C and D. For well-posed linear systems with unbounded generators these formulae will not always be well-defined. Instead, we suggest another approach for the class of well-posed linear systems f...

We define the domain of a linear fractional transformation in a space of operators and show that both the affine automorphisms and the compositions of symmetries act transitively on these domains. Further, we show that Liouville’s theorem holds for domains of linear fractional transformations and, with an additional trace class condition, so does the Riemann removable singularities theorem. We ...