Freeden W., Zuhair Nashed M. Handbook of Mathematical Geodesy: Functional Analytic and Potential Theoretic Methods

Basel: Birkhauser, 2018. — 938 p. — ISBN 978-3-319-57181-2.Written by leading experts, this book provides a clear and comprehensive survey of the “status quo” of the interrelating process and cross-fertilization of structures and methods in mathematical geodesy. Starting with a foundation of functional analysis, potential theory, constructive approximation, special function theory, and inverse problems, readers are subsequently introduced to today’s least squares approximation, spherical harmonics reflected spline and wavelet concepts, boundary value problems, Runge-Walsh framework, geodetic observables, geoidal modeling, ill-posed problems and regularizations, inverse gravimetry, and satellite gravity gradiometry. All chapters are self-contained and can be studied individually, making the book an ideal resource for both graduate students and active researchers who want to acquaint themselves with the mathematical aspects of modern geodesy.Preface.
Introduction.
Gauss as Scientific Mediator Between Mathematics and Geodesy from the Past to the Present.
An Overview on Tools from Functional Analysis.
Ill-Posed Problems: Operator Methodologies of Resolution and Regularization.
Geodetic Observables and Their Mathematical Treatment in Multiscale Framework.
The Analysis of the Geodetic Boundary Value Problem: State and Perspectives.
Oblique Stochastic Boundary Value Problem.
About the Importance of the Runge – Walsh Concept for Gravitational Field Determination.
Geomathematical Advances in Satellite Gravity Gradiometry (SGG).
Parameter Choices for Fast Harmonic Spline Approximation.
Inverse Gravimetry as an Ill-Posed Problem in Mathematical Geodesy.
Gravimetry and Exploration.
Spherical Harmonics Based Special Function Systems and Constructive Approximation Methods.
Spherical Potential Theory: Tools and Applications.
Joint Inversion of Multiple Observations.
On the Non-Uniqueness of Gravitational and Magnetic Field Data Inversion (Survey Article).
Index.