Austrian Academy of Sciences
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On multidimensional sinc-Gauss sampling formulas for analytic functions. ETNA - Electronic Transactions on Numerical Analysis
Using complex analysis, we present new error estimates for multidimensional sinc-Gauss sampling formulas for multivariate analytic functions and their partial derivatives, which are valid for wide classes of functions. The first class consists of all n-variate entire functions of exponential type satisfying a decay condition, while the second is the class of n-variate analytic functions defined on a multidimensional horizontal strip. We show that the approximation error decays exponentially with respect to the localization parameter N. This work extends former results of the first author and J. Prestin, [IMA J. Numer. Anal., 36 (2016), pp. 851–871] and [Numer. Algorithms, 86 (2021), pp. 1421–1441], on two-dimensional sinc-Gauss sampling formulas to the general multidimensional case. Some numerical experiments are presented to confirm the theoretical analysis
Die Gerichtsbarkeit der Prager Altstadt und der vereinten Prager Städte in der Zeit der Jagiellonen (1471–1526). Beiträge zur Rechtsgeschichte Österreichs|Beiträge zur Rechtsgeschichte Österreichs Band 2 / 2020|
The purpose of this contribution is to present a research project on the judiciary of the Old Town of Prague and the United Prague towns in the time of the Jagiellons and some of its preliminary results. The main starting‐point as to the investigated sources is represented by sentences and verdicts of the town court of the Old Town of Prague from 1475–1518 and by sentences and verdicts intimated by the town court of the United Prague towns from 1518–1526. The sentences and verdicts passed in those years are found predominantly in the Books of verdicts (libri sententiarum). From the entire number of 1,004 registered sentences in law‐suits, 533 were passed by the town court of the Old Town in 1475–1518, and 471 by the town court of the United Prague towns in 1518–1526. From those 1,004 sentences, 257 (25.6 %) concern criminal cases. Also in the paper, the results of the analysis of the abovementioned criminal cases are presented. The analysis led to the conclusion that the greater part of the criminal agenda of the courts under investigation consisted of criminal acts against life and health and honour. Offences against property occurred only in relatively smaller numbers. Regarding the development of town law it is possible to register during the Jagellonian era a conspicuous improvement concerning the adjucative practice of the court of the Old Town. This improvement was reflected also in a better quality and more refined forms of decisions rendered by the court. Whereas the Old Town law is to be regarded from the point of view of its development as representing at the outset of the Jagellonian era in considerable measure an autochthonous legal system sui generis taking over only in an unsystematic way and ad hoc the norms of the south German and Magdeburg town laws, the first tenth of the epoch in question in the Old Town was characterised by the broad and intense taking over of the conspicuously more developed town law of Brno (Brünn) and of Roman law too. Towards the end of the Jagellonian era, this takeover in the Prague towns was completed not only at the theoretical level, but also in the sphere of legal practice, thereby creating one of the central preconditions for the later codification of the Bohemian town law (1579)
Mitteleuropäisches Zivilrecht. Studien und Beiträge zum ADHGB. Beiträge zur Rechtsgeschichte Österreichs|Beiträge zur Rechtsgeschichte Österreichs Band 2 / 2020|
The General German Commercial Code (ADHGB) of 1861 defined in the second half of the 19th century the course of business in Central Europe, assuming substantially the function of a common Law of Obligations. As a “Uniform Act” it provided the Sale of Goods with a comprehensive set of rules, formative for the further development in the 20th century