We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We employ two types of Tauberian hypotheses; the first kind involves distributional boundedness, while the second type imposes a one-sided assumption on the Cesàro behavior of the distribution. We apply these Tauberian results to deduce a number of Tauberian theorems for power series and Stieltjes integrals where Cesàro summability follows from Abel summability. We also use our general results to give a new simple proof of the classical Littlewood one-sided Tauberian theorem for power series.
The perception of danger represents a crucial component of everyday life (not only) in the city. The recording of the development of perception of danger in diachronic perspective of the twentieth century, as it reflected in the memory of the female inhabitants of Pilsen, enables to ascertain some changes that reflect the historical development. In its concrete parts, the research focused on the modes of „making“ of the urban space through the perception of danger (mental topography of danger), the perception of danger in general, as wall as the impact of the danger on the everyday life of the inhabitants. The qualitative methodology of the research included the making of mental maps and the half-structured interviews. The informers were nine women of age 80–91 years. For the purpose of presentation of the results of the research that aimed at ascertaining the ways of perceiving danger by the oldest generation of female inhabitants of Pilsen, the twentieth century was divided into several periods that to great degree reflected the political-historical development: the period before the Second World War; the period of the war; after-war period (1945–1960), the 1960s to 1980s and finally the period after the year 1990 up to the present. In the memory of the informers, these periods were characterized partly by differing types of danger (if danger at all) and their varying intensity. The perception of danger (or the absence of danger) was also influenced by the different development of life cycles in cases of concrete women. Besides individual differences, there was crucial influence of the general social development, the development of the city and the technological development, especially the increase of automobile transport and the media of communication.