000193623 001__ 193623 000193623 003__ CZ-ZdVUG 000193623 005__ 20190206110311.0 000193623 041__ $$aeng 000193623 040__ $$aABC039$$bcze 000193623 1001_ $$aHolota, Petr 000193623 24510 $$aSummation of series and an approximation of Legendre?s functions in constructing integral kernels for the exterior of an ellipsoid: Application to boundary value problems in physical geodesy 000193623 300__ $$a12 stran 000193623 5203_ $$aThe paper primarily concerns physical geodesy applications and thus problems associated with Laplace?s and Poisson?s partial differential equation that offer a natural basis for gravity field studies. In the introduction a brief review is given on Green?s function constructed for Stokes? and Neumann?s problem formulated for the exterior of a sphere. The second of the problems is considered also within the weak solution concept. Galerkin elements are expressed for the special case when the function basisis generated by the respective reproducing kernel or represented by reciprocal distances (elementary potentials). The solution domain is then generalized and the paper focuses on the construction of the reproducing kernel of Hilbert?s space of functionsharmonic in the exterior of an oblate ellipsoid of revolution. In the first stage the kernel is represented by a series of ellipsoidal harmonics. 000193623 655_4 $$ačlánek v odborném periodiku 000193623 7730_ $$92015$$dSpolková republika Německo$$g19 (2015), 12 s.$$tLeibniz Online$$x1863-3285 000193623 85642 $$ahttps://www.rvvi.cz/riv?s=rozsirene-vyhledavani&ss=detail&n=0&h=RIV%2F00025615%3A_____%2F15%3A%230002185%21RIV16-GA0-00025615 000193623 910__ $$aABC039 000193623 980__ $$aclanky_vugtk 000193623 985__ $$aholota 000193623 985__ $$ariv 000193623 985__ $$autvar24