Willi Freeden's Books

Geomathematically Oriented Potential Theory

By: Willi Freeden,Christian Gerhards

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Geomathematically Oriented Potential Theory

By: Willi Freeden,Christian Gerhards

As the Earth`s surface deviates from its spherical shape by less than 0.4 percent of its radius and today’s satellite missions collect their gravitational and magnetic data on nearly spherical orbits, sphere-oriented mathematical methods and tools play important roles in studying the Earth’s gravitational and magnetic field. Geomathematically Oriented Potential Theory presents the principles of space and surface potential theory involving Euclidean and spherical concepts. The authors offer new insight on how to mathematically handle gravitation and geomagnetism for the relevant observables and how to solve the resulting potential problems in a systematic, mathematically rigorous framework. The book begins with notational material and the necessary mathematical background. The authors then build the foundation of potential theory in three-dimensional Euclidean space and its application to gravitation and geomagnetism. They also discuss surface potential theory on the unit sphere along with corresponding applications. Focusing on the state of the art, this book breaks new geomathematical grounds in gravitation and geomagnetism. It explores modern sphere-oriented potential theoretic methods as well as classical space potential theory.

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470

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CRC Press

Published Date

ISBN 10

1439895422

ISBN 13

9781439895429

Integration and Cubature Methods

A Geomathematically Oriented Course

By: Willi Freeden,Martin Gutting

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Integration and Cubature Methods

A Geomathematically Oriented Course

By: Willi Freeden,Martin Gutting

In industry and economics, the most common solutions of partial differential equations involving multivariate numerical integration over cuboids include techniques of iterated one-dimensional approximate integration. In geosciences, however, the integrals are extended over potato-like volumes (such as the ball, ellipsoid, geoid, or the Earth) and their boundary surfaces which require specific multi-variate approximate integration methods. Integration and Cubature Methods: A Geomathematically Oriented Course provides a basic foundation for students, researchers, and practitioners interested in precisely these areas, as well as breaking new ground in integration and cubature in geomathematics.

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501

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CRC Press

Published Date

ISBN 10

1351764764

ISBN 13

9781351764766

Multiscale Potential Theory

With Applications to Geoscience

By: Willi Freeden,Volker Michel

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Multiscale Potential Theory

With Applications to Geoscience

By: Willi Freeden,Volker Michel

This self-contained text/reference provides a basic foundation for practitioners, researchers, and students interested in any of the diverse areas of multiscale (geo)potential theory. New mathematical methods are developed enabling the gravitational potential of a planetary body to be modeled using a continuous flow of observations from land or satellite devices. Harmonic wavelets methods are introduced, as well as fast computational schemes and various numerical test examples. Presented are multiscale approaches for numerous geoscientific problems, including geoidal determination, magnetic field reconstruction, deformation analysis, and density variation modelling With exercises at the end of each chapter, the book may be used as a textbook for graduate-level courses in geomathematics, applied mathematics, and geophysics. The work is also an up-to-date reference text for geoscientists, applied mathematicians, and engineers.

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522

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Springer Science & Business Media

Published Date

ISBN 10

1461220483

ISBN 13

9781461220480

Lattice Point Identities and Shannon-Type Sampling

By: Willi Freeden,M. Zuhair Nashed

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Lattice Point Identities and Shannon-Type Sampling

By: Willi Freeden,M. Zuhair Nashed

Lattice Point Identities and Shannon-Type Sampling demonstrates that significant roots of many recent facets of Shannon's sampling theorem for multivariate signals rest on basic number-theoretic results. This book leads the reader through a research excursion, beginning from the Gaussian circle problem of the early nineteenth century, via the classical Hardy-Landau lattice point identity and the Hardy conjecture of the first half of the twentieth century, and the Shannon sampling theorem (its variants, generalizations and the fascinating stories about the cardinal series) of the second half of the twentieth century. The authors demonstrate how all these facets have resulted in new multivariate extensions of lattice point identities and Shannon-type sampling procedures of high practical applicability, thereby also providing a general reproducing kernel Hilbert space structure of an associated Paley-Wiener theory over (potato-like) bounded regions (cf. the cover illustration of the geoid), as well as the whole Euclidean space. All in all, the context of this book represents the fruits of cross-fertilization of various subjects, namely elliptic partial differential equations, Fourier inversion theory, constructive approximation involving Euler and Poisson summation formulas, inverse problems reflecting the multivariate antenna problem, and aspects of analytic and geometric number theory. Features: New convergence criteria for alternating series in multi-dimensional analysis Self-contained development of lattice point identities of analytic number theory Innovative lattice point approach to Shannon sampling theory Useful for students of multivariate constructive approximation, and indeed anyone interested in the applicability of signal processing to inverse problems.

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287

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CRC Press

Published Date

ISBN 10

1000757749

ISBN 13

9781000757743

Inverse Magnetometry

Mollifier Magnetization Distribution from Geomagnetic Field Data

By: Christian Blick,Willi Freeden,M. Zuhair Nashed,Helga Nutz,Michael Schreiner

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Inverse Magnetometry

Mollifier Magnetization Distribution from Geomagnetic Field Data

By: Christian Blick,Willi Freeden,M. Zuhair Nashed,Helga Nutz,Michael Schreiner

This monograph presents the geoscientific context arising in decorrelative geomagnetic exploration. First, an insight into the current state of research is given by reducing magnetometry to mathematically accessible, and thus calculable, decorrelated models. In this way, various questions and problems of magnetometry are made available to a broad scientific audience and the exploration industry. New stimuli are given, and innovative ways of modeling geologic strata by mollifier magnetometric techniques are shown. Potential data sets primarily of terrestrial origin constitute the main data basis in the book. For deep geology, the geomathematical decorrelation methods are designed in such a way that depth information (e.g., in boreholes) may be canonically entered. Overall, this book provides pioneering and ground-breaking innovative mathematical knowledge as a transfer methodology from the “reality space” of magnetometric measurements into the “virtual space” of mathematical-numerical modeling structures and mollifier solutions with novel geological application areas. It pursues a double goal: On the one hand, it represents a geoscientific set of rules for today's geoengineering, interested in the application of innovative modelling and simulation techniques to promising data sets and structures occurring in geomagnetics. On the other hand, the book serves as a collection of current material in Applied Mathematics to offer alternative methodologies in the theory of inverse problems.

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114

Publisher

Springer Nature

Published Date

ISBN 10

303079508X

ISBN 13

9783030795085

Spherical Functions of Mathematical Geosciences

A Scalar, Vectorial, and Tensorial Setup

By: Willi Freeden,Michael Schreiner

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Spherical Functions of Mathematical Geosciences

A Scalar, Vectorial, and Tensorial Setup

By: Willi Freeden,Michael Schreiner

In recent years, the Geomathematics Group, TU Kaiserslautern, has worked to set up a theory of spherical functions of mathematical physics. This book is a collection of all the material that group generated during the process.

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609

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Springer Science & Business Media

Published Date

ISBN 10

3540851127

ISBN 13

9783540851127

Metaharmonic Lattice Point Theory

By: Willi Freeden

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Metaharmonic Lattice Point Theory

By: Willi Freeden

Metaharmonic Lattice Point Theory covers interrelated methods and tools of spherically oriented geomathematics and periodically reflected analytic number theory. The book establishes multi-dimensional Euler and Poisson summation formulas corresponding to elliptic operators for the adaptive determination and calculation of formulas and identities of

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467

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CRC Press

Published Date

ISBN 10

1439861854

ISBN 13

9781439861851

The Fourth Ordeal

A History of the Muslim Brotherhood in Egypt, 19682018

By: Victor J. Willi

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The Fourth Ordeal

A History of the Muslim Brotherhood in Egypt, 19682018

By: Victor J. Willi

A history of the Muslim Brotherhood in Egypt based on first-person interviews with Brotherhood rank-and-file members.

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489

Publisher

Cambridge University Press

Published Date

ISBN 10

1108830641

ISBN 13

9781108830645

Spherical Sampling

By: Willi Freeden,M. Zuhair Nashed,Michael Schreiner

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Spherical Sampling

By: Willi Freeden,M. Zuhair Nashed,Michael Schreiner

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.

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591

Publisher

Birkhäuser

Published Date

ISBN 10

3319714589

ISBN 13

9783319714585

Recovery Methodologies: Regularization and Sampling

By: Willi Freeden,M. Zuhair Nashed

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Recovery Methodologies: Regularization and Sampling

By: Willi Freeden,M. Zuhair Nashed

The goal of this book is to introduce the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. The recovery of objects from a set of data demands key solvers of inverse and sampling problems. Until recently, connections between the mathematical areas of inverse problems and sampling were rather tenuous. However, advances in several areas of mathematical research have revealed deep common threads between them, which proves that there is a serious need for a unifying description of the underlying mathematical ideas and concepts. Freeden and Nashed present an integrated approach to resolution methodologies from the perspective of both these areas. Researchers in sampling theory will benefit from learning about inverse problems and regularization methods, while specialists in inverse problems will gain a better understanding of the point of view of sampling concepts. This book requires some basic knowledge of functional analysis, Fourier theory, geometric number theory, constructive approximation, and special function theory. By avoiding extreme technicalities and elaborate proof techniques, it is an accessible resource for students and researchers not only from applied mathematics, but also from all branches of engineering and science.

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505

Publisher

American Mathematical Society

Published Date

ISBN 10

1470473453

ISBN 13

9781470473457

Spherical Functions of Mathematical Geosciences

A Scalar, Vectorial, and Tensorial Setup

By: Willi Freeden,Michael Schreiner

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Spherical Functions of Mathematical Geosciences

A Scalar, Vectorial, and Tensorial Setup

By: Willi Freeden,Michael Schreiner

This book is an enlarged second edition of a monograph published in the Springer AGEM2-Series, 2009. It presents, in a consistent and unified overview, a setup of the theory of spherical functions of mathematical (geo-)sciences. The content shows a twofold transition: First, the natural transition from scalar to vectorial and tensorial theory of spherical harmonics is given in a coordinate-free context, based on variants of the addition theorem, Funk-Hecke formulas, and Helmholtz as well as Hardy-Hodge decompositions. Second, the canonical transition from spherical harmonics via zonal (kernel) functions to the Dirac kernel is given in close orientation to an uncertainty principle classifying the space/frequency (momentum) behavior of the functions for purposes of data analysis and (geo-)application. The whole palette of spherical functions is collected in a well-structured form for modeling and simulating the phenomena and processes occurring in the Earth's system. The result is a work which, while reflecting the present state of knowledge in a time-related manner, claims to be of largely timeless significance in (geo-)mathematical research and teaching.

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729

Publisher

Springer Nature

Published Date

ISBN 10

3662656922

ISBN 13

9783662656921

Special Functions of Mathematical (Geo-)Physics

By: Willi Freeden,Martin Gutting

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Special Functions of Mathematical (Geo-)Physics

By: Willi Freeden,Martin Gutting

Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis. Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises.

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505

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Springer Science & Business Media

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ISBN 10

3034805632

ISBN 13

9783034805636

Geomathematically Oriented Potential Theory

By: Willi Freeden,Christian Gerhards

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Geomathematically Oriented Potential Theory

By: Willi Freeden,Christian Gerhards

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470

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CRC Press

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1439895422

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9781439895429

Multiscale Potential Theory

With Applications to Geoscience

By: Willi Freeden,Volker Michel

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Multiscale Potential Theory

With Applications to Geoscience

By: Willi Freeden,Volker Michel

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522

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Springer Science & Business Media

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1461220483

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9781461220480

Recovery Methodologies: Regularization and Sampling

By: Willi Freeden,M. Zuhair Nashed

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Recovery Methodologies: Regularization and Sampling

By: Willi Freeden,M. Zuhair Nashed

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505

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American Mathematical Society

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1470473453

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9781470473457

Lattice Point Identities and Shannon-Type Sampling

By: Willi Freeden,M. Zuhair Nashed

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Lattice Point Identities and Shannon-Type Sampling

By: Willi Freeden,M. Zuhair Nashed

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287

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CRC Press

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1000757749

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9781000757743

Exploratory Potential Methods in Geothermal Power Generation

A Survey on Innovative Gravimetry and Magnetometry

By: Willi Freeden,Helga Nutz

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Exploratory Potential Methods in Geothermal Power Generation

A Survey on Innovative Gravimetry and Magnetometry

By: Willi Freeden,Helga Nutz

The book provides the geoscientific context, that arises in gravimetric/magnetometric exploration. It essentially uses mathematics as a key technology for modeling issues on the basis of analysis and interpretation according to dense and precise gravitational/magnetic measurements. It is dedicated to surface and deep geology with potential data primarily of terrestrial origin. The book spans the interdisciplinary arc from geoengineering, especially geodesy, via geophysics to geomathematics and geology, and back again. It presents the recently published pioneering and groundbreaking multiscale mollifier methodologies realizing the bridging transfer from gravitational/magnetic measurements to approximative/numerical mollifier wavelet decorrelations with novel geologic prospects and layer-structure determination as outcome. Using the specific example of the German Saarland region, new important fields of application, especially for areas with mining-related cavities, will be opened up and subjected to an in-depth geologic detection.

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224

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Springer Nature

Published Date

ISBN 10

3031544129

ISBN 13

9783031544125

Inverse Magnetometry

Mollifier Magnetization Distribution from Geomagnetic Field Data

By: Christian Blick,Willi Freeden,M. Zuhair Nashed,Helga Nutz,Michael Schreiner

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Inverse Magnetometry

Mollifier Magnetization Distribution from Geomagnetic Field Data

By: Christian Blick,Willi Freeden,M. Zuhair Nashed,Helga Nutz,Michael Schreiner

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114

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Springer Nature

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ISBN 10

303079508X

ISBN 13

9783030795085

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