Handbook of Mathematical Geodesy

Functional Analytic and Potential Theoretic Methods

Willi Freeden, M. Zuhair Nashed (Herausgeber)

Buch | Hardcover

XIV, 932 Seiten

2018 | 1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-57179-9 (ISBN)

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lt;p>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.

Willi Freeden is Professor of Geomathematics at the Technical University of Kaiserslautern, GermanyZuhair Nahed is Professor at the University of Central Florida, Orlando, USA

lt;p>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.

lt;p>"The Handbook of Mathematical Geodesy presents for the mathematicians a wealth of applications and for the geodesists a solid embedding of the fundamental concepts of physical geodesy into approximation theory." (Karl-Rudolf Koch, Journal of Geodesy, Vol. 93, 2019)

"The Handbook of Mathematical Geodesy presents a remarkable achievement. The book bridges the gap between the abstract work of the mathematicians and the practically oriented measurements of the geodesists. ... the book is broadly planned, and it presents the present state of knowledge." (Karl-Rudolf Koch, International Journal on Geomathematics GEM, Vol. 10, 2019)

Erscheinungsdatum	27.06.2018
Reihe/Serie	Geosystems Mathematics
Zusatzinfo	XIV, 932 p. 155 illus., 76 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1521 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Naturwissenschaften ► Geowissenschaften ► Geophysik
Schlagworte	Abstract harmonic analysis • Complex analysis, complex variables • Constructive Approximation • determination of the shape of the Earth • Differential calculus & equations • Differential calculus & equations • Geophysics • Geophysics/Geodesy • gravitational field determination • inference theory and geodetic networks • Inverse Problems • Mathematics • mathematics and statistics • Partial differential equations • satellite methods
ISBN-10	3-319-57179-6 / 3319571796
ISBN-13	978-3-319-57179-9 / 9783319571799
Zustand	Neuware