000193622 001__ 193622 000193622 003__ CZ-ZdVUG 000193622 005__ 20190118105509.0 000193622 040__ $$aABC039$$bcze 000193622 1001_ $$aHolota, Petr 000193622 24510 $$aSummation of series and an approximation of Legendre?s functions in constructing integral kernels for the exterior of an ellipsoid: Application to boundary value problems in physical geodesy 000193622 5203_ $$aThe paper primarily concerns physical geodesy applications and thus problems associated with Laplace?s and Poisson?s partial differential equation that offer a natural basis for gravity field studies. In the introduction a brief review is given on Green?s function constructed for Stokes? and Neumann?s problem formulated for the exterior of a sphere. The second of the problems is considered also within the weak solution concept. Galerkin elements are ex-pressed for the special case when the function basis is generated by the respective reproduc-ing kernel or represented by reciprocal distances (elementary potentials). The solution do-main is then generalized and the paper focuses on the construction of the reproducing kernel of Hilbert?s space of functions harmonic in the exterior of an oblate ellipsoid of revolution. In the first stage the kernel is represented by a series of ellipsoidal harmonics. However, the manipulation with the series and a numerical implementation of the integral 000193622 655_4 $$aAudiovizuální tvorba 000193622 7730_ $$92015$$dBerlín:Leibniz Society of Science at Berlin,2015. 000193622 85642 $$ahttps://www.rvvi.cz/riv?s=rozsirene-vyhledavani&ss=detail&n=0&h=RIV%2F00025615%3A_____%2F15%3A%230002192%21RIV16-GA0-00025615 000193622 910__ $$aABC039 000193622 980__ $$aclanky_vugtk 000193622 985__ $$aholota 000193622 985__ $$ariv 000193622 985__ $$autvar24