About: Green’s Function, Reproducing Kernel and Galerkin’s Matrix for the Exterior of an Ellipsoid: Application in Gravity Field Studies

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Description	In the introductory part the importance of the topic for gravity field studies is outlined. Concepts and tools used for the representation of solutions of boundary value problems are mentioned. A weak formulation of Neumann’s problem is considered with emphasis on function bases generated by the reproducing kernel of Hilbert’s space of functions. The paper then focuses on the reproducing kernel for the solution domain given by the exterior of an oblate ellipsoid of revolution. First its exact structure is derived by means of the apparatus of ellipsoidal harmonics. In this case the structure of the kernel, similarly as of the entries of Galerkin’s matrix, becomes rather complex. Therefore, an approximation of ellipsoidal harmonics based on an approximation version of Legendre’s ordinary differential equation (limit layer approach) is used. A numerical implementation of the exact structure of the reproducing kernel is mention as a driving impulse of running investigations. In the introductory part the importance of the topic for gravity field studies is outlined. Concepts and tools used for the representation of solutions of boundary value problems are mentioned. A weak formulation of Neumann’s problem is considered with emphasis on function bases generated by the reproducing kernel of Hilbert’s space of functions. The paper then focuses on the reproducing kernel for the solution domain given by the exterior of an oblate ellipsoid of revolution. First its exact structure is derived by means of the apparatus of ellipsoidal harmonics. In this case the structure of the kernel, similarly as of the entries of Galerkin’s matrix, becomes rather complex. Therefore, an approximation of ellipsoidal harmonics based on an approximation version of Legendre’s ordinary differential equation (limit layer approach) is used. A numerical implementation of the exact structure of the reproducing kernel is mention as a driving impulse of running investigations. (en)
Title	Green’s Function, Reproducing Kernel and Galerkin’s Matrix for the Exterior of an Ellipsoid: Application in Gravity Field Studies Green’s Function, Reproducing Kernel and Galerkin’s Matrix for the Exterior of an Ellipsoid: Application in Gravity Field Studies (en)
skos:prefLabel	Green’s Function, Reproducing Kernel and Galerkin’s Matrix for the Exterior of an Ellipsoid: Application in Gravity Field Studies Green’s Function, Reproducing Kernel and Galerkin’s Matrix for the Exterior of an Ellipsoid: Application in Gravity Field Studies (en)
skos:notation	RIV/00025615:_____/10:#0001716!RIV11-CUZ-00025615
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(LC506), Z(CUZ0002561501)
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Holota, Petr
http://linked.open.../riv/druhVysledku	A(V) - Audiovizuální tvorba se vzdáleným přístupem
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Výzkumný ústav geodetický, topografický a kartografický, v.v.i.
http://linked.open...dnocenehoVysledku	261020
http://linked.open...ai/riv/idVysledku	RIV/00025615:_____/10:#0001716
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Earth’s gravity field; Geodetic boundary value problems; Green’s functions; Variational methods; Reproducing kernels (en)
http://linked.open.../riv/klicoveSlovo	Earth’s gravity field Green’s functions Geodetic boundary value problems Reproducing kernels Variational methods
http://linked.open...i/riv/kodPristupu	L
http://linked.open...ontrolniKodProRIV	[7D95A0F123F1]
http://linked.open...i/riv/mistoVydani	Vídeň
http://linked.open...telVyzkumneZpravy	European Geoscience Union
http://linked.open...in/vavai/riv/obor	DE
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Recent dynamics of the Earth
http://linked.open...UplatneniVysledku	2010
http://linked.open...iv/tvurceVysledku	Holota, Petr
http://linked.open...n/vavai/riv/zamer	Research and Development in Geodesy, Cadastre and Geomatics in 2005 - 2011

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