On the Schwartz space isomorphism theorem for the Riemannian symmetric spaces

We deduce a proof of the isomorphism theorem for certain closed subspace \mc S^p_\Gamma(X) of the $L^p$-Schwartz class functions $(0< p \leq 2)$ on a Riemannian symmetric space $X$ where $\Gamma$ is a finite subset of \what{K}_M. The Fourier transform considered is the Helgason Fourier transform. Our proof relies only on the Paley-Wiener theorem for the corresponding class of functions and hence it does not use the complicated higher asymptotics of the elementary spherical functions.Comment: 23 page

Stability of Neutral Delay Differential Equations and Their Discretizations

Disertační práce se zabývá asymptotickou stabilitou zpožděných diferenciálních rovnic a jejich diskretizací. V práci jsou uvažovány lineární zpožděné diferenciální rovnice s~konstantním i neohraničeným zpožděním. Jsou odvozeny nutné a postačující podmínky popisující oblast asymptotické stability jak pro exaktní, tak i diskretizovanou lineární neutrální diferenciální rovnici s konstantním zpožděním. Pomocí těchto podmínek jsou porovnány oblasti asymptotické stability odpovídajících exaktních a diskretizovaných rovnic a vyvozeny některé vlastnosti diskrétních oblastí stability vzhledem k měnícímu se kroku použité diskretizace. Dále se zabýváme lineární zpožděnou diferenciální rovnicí s neohraničeným zpožděním. Je uveden popis jejích exaktních a diskrétních oblastí asymptotické stability spolu s asymptotickým odhadem jejich řešení. V závěru uvažujeme lineární diferenciální rovnici s více neohraničenými zpožděními.The doctoral thesis discusses the asymptotic stability of delay differential equations and their discretizations. The linear delay differential equations with constant as well as infinite lag are considered. The necessary and sufficient conditions describing the asymptotic stability region of both exact and discretized linear neutral delay differential equation with constant lag are derived. We compare asymptotic stability domains of corresponding exact and discretized equations and discuss properties of derived stability regions with respect to a changing stepsize of the utilized discretization. Further, we investigate the linear delay differential equation with the infinite lag. We present the description of its exact and discrete asymptotic stability regions together with asymptotic estimates of its solutions. The linear delay differential equation with several infinite lags is discussed as well.

Komunikace – významný prostředek nespokojenosti managementu

Purpose of the article: Effective communication in an organization is one of the preconditions of its operation. The aim of the article is to point out the communication process in the complaints management, to emphasize importance of the communication in the business practice and the current state analyze of the communication in Slovak business subjects. The paper presents the partial results and conclusions of research carried out. Methodology/methods: The methodology of this study is based on the scientific methods of acquiring and processing data – observation, questionnaire, interview, qualitative methods (analysis, synthesis, induction, deduction, comparison, abstraction, etc.); quantitative methods (descriptive statistics such as frequency analysis, statistical analysis, confidence intervals) and graphical methods. Scientific aim: The scientific aim of the article is to prove the established differences between business subjects that are the result of systematic influence (for example quality management system, subject of business, duration of action in the market). Findings: The research results have revealed the strengths of business subjects and revealed the areas which need to be improved. In the first place, they should become aware of the fact that the communication process necessarily forms the part of the complaints management and is well founded. The positive effect also has implementation of the existing ISO 9000 series of standards into business practice, which was reflected in a higher level of complaints management. Conclusions: Following the knowledge of communication process and its functioning plus awareness of communication obstacles, it is possible to improve the effectiveness and the result of communication and by that affect the overall result of claim procedure. Therefore, communication can be considered as very significant element in the process of complaints and claims handling