Titlebook: Mathematische Geodäsie/Mathematical Geodesy; Handbuch der Geodäsi Willi Freeden Book 2020 Springer-Verlag GmbH Deutschland, ein Teil von Sp

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Theory and Realization of Reference Systemsalso those of the rich geodetic theory are presented, based on the fact that the physical cause of the rank deficiency is known to be the lack of definition of the reference system. The additional geodetic results are based on the fact that one can easily construct a matrix with columns that are a b

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Inverse Probleme der Geodäsiehtlich Existenz, Eindeutigkeit und Stabilität eines Lösungsprozesses werden beschrieben. Die Notwendigkeit zur Regularisierung wird herausgestellt, spezifische Eigenschaften der Regularisierungsverfahren werden kurz skizziert.

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Up and Down Through the Gravity Field is to describe the properties of the propagation of the potential, or of its relevant functionals, while moving upward or downward. The upward propagation is always a properly posed problem, in fact a smoothing and somehow related to the Newton integral and to the solution of boundary value problem

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Spherical Harmonics, Splines, and Waveletsolving spherical harmonics, splines, and wavelets, thereby establishing a consistent and unified setup. The goal of the work is to preferably convince members from geodesy that spherically oriented approximation provides a rich mathematical cornucopia that has much to offer to a large palette of app

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A Mathematical View on Spin-Weighted Spherical Harmonics and Their Applications in Geodesytions. Mainly, they are used in quantum mechanics and geophysics for the theory of gravitation and in early universe and classical cosmology. Furthermore, they have also applications in geodesy. The quantity of formulations conditioned this huge spectrum of versatility. Formulations we use are for e

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Reconstruction and Decomposition of Scalar and Vectorial Potential Fields on the Sphererelated to potential field problems and spatial localization, such as spherical splines, multiscale methods, and Slepian functions. Furthermore, we introduce the common Helmholtz and Hardy-Hodge decompositions of spherical vector fields together with some related recent results. The methods are illu

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