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Handbook of Mathematical Geodesy: Functional Analytic and Potential Theoretic Methods

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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.

Authors: Freeden Michael, Nahed Zuhair
Publisher: BIRKHAUSER
Pages: 932
ISBN: 9783030096229
Cover: Paperback
Edition Number: 1
Release Year: 2018

Introduction.- Gauss as Scientific Mediator between Mathematics and Geodesy from the Past to the Present​.- An Overview on Tools from Functional Analysis.- Operator-Theoretic and Regularization Approaches to Ill-Posed Problems.- Geodetic Observables and Their Mathematical Treatment in Multiscale Framework.- The Analysis of 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.- Parameter Choices for Fast Harmonic Spline Approximation.- Gravimetry as an Ill-Posed Problem in Mathematical Geodesy.- Gravimetry and Exploration.- On the Non-Uniqueness of Gravitational and Magnetic Field Data Inversion.- Spherical Harmonics Based Special Function Systems and Constructive Approximation Methods.- Spherical Potential Theory: Tools and Applications.- A combination of Downward Continuation and Local Approximation for Harmonic Potentials.- Joint Inversion of Multiple Observation.

Michael Freeden is Professor of Political Theory at the University of Nottingham and Emeritus Professor of Politics, University of Oxford. His books include The New Liberalism: An Ideology of Social Reform (Oxford, 1978); Liberalism Divided: A Study in British Political Thought 1914-1939 (Oxford, 1986); Ideologies and Political Theory: A Conceptual Approach (Oxford, 1996); Ideology: A Very Short Introduction (Oxford, 2003); Liberal Languages: Ideological Imaginations and 20th Century Progressive Thought (Princeton, 2005); The Political Theory of Political Thinking (Oxford, 2013), and The Oxford Handbook of Political Ideologies (co-edited, Oxford, 2013). He is the founder-editor of the Journal of Political Ideologies. In 2012 he was awarded the Sir Isaiah Berlin Prize for Lifetime Contribution to Political Studies by the UK Political Studies Association and the Medal for Science of the Institute of Advanced Studies, Bologna University.

Zuhair Nahed is Professor at the University of Central Florida, Orlando, USA

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