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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.

Mathematics. --- Geophysics. --- Harmonic analysis. --- Partial differential equations. --- Abstract Harmonic Analysis. --- Geophysics/Geodesy. --- Partial Differential Equations. --- Geodesy --- Physical geography. --- Differential equations, partial. --- Partial differential equations --- Geography --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Geological physics --- Terrestrial physics --- Earth sciences --- Physics

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This book presents, in a consistent and unified overview, results and developments in the field of today´s spherical sampling, particularly arising in mathematical geosciences. Although the book often refers to original contributions, the authors made them accessible to (graduate) students and scientists not only from mathematics but also from geosciences and geoengineering. Building a library of topics in spherical sampling theory it shows how advances in this theory lead to new discoveries in mathematical, geodetic, geophysical as well as other scientific branches like neuro-medicine. A must-to-read for everybody working in the area of spherical sampling.

Mathematics. --- Geophysics. --- Partial differential equations. --- Special functions. --- Information theory. --- Numerical analysis. --- Mathematics --- Special Functions. --- Partial Differential Equations. --- Numerical Analysis. --- Geophysics/Geodesy. --- Information and Communication, Circuits. --- Mathematics Education. --- Study and teaching. --- Functions, special. --- Differential equations, partial. --- Physical geography. --- Geography --- Partial differential equations --- Mathematical analysis --- Math --- Science --- Special functions --- Mathematics—Study and teaching . --- Communication theory --- Communication --- Cybernetics --- Geological physics --- Terrestrial physics --- Earth sciences --- Physics