Spherical sampling
type: Item
instance of: scholarly article
title: Spherical sampling
zbMATH Open document ID: 1396.86002
DOI: 10.1007/978-3-319-71458-5
author: Willi Freeden
author: M. Zuhair Nashed
author: Michael Schreiner
published in: Geosystems Mathematics
publication date: 2018-04-23T00:00:00Z
review text: The authors have many years of experience in the field of geomathematics and now present a mathematically demanding textbook on spherically reflected sampling under geomathematically significant aspects. From the Preface: The major purpose is to give a consistent and unified overview of diverse results and various developments in the field of today's spherical sampling, particularly those arising in mathematical geosciences such as mathematical geodesy and geophysics. Although the book often refers to original contributions, we have tried to make it accessible to (graduate) students and scientists not only from mathematics but also from geosciences and geoengineering interesed in spherical sampling theory and to show how advances in this theory lead to new discoveries in mathematical, geodetic, geophysical as well as other scientific branches, for example, neuro-medicine. From the Introduction: The special interest in writing this monograph is to specify and classify general sampling types of polynomial (i.e. spherical harmonics) expansion, spline interpolation, and wavelet approximation on the unit sphere corresponding to structured and scattered data. The large class of possible weights that are permitted in bandlimited polynomial as well as non-bandlimited spline sampling should allow the users to built up some desirable characterisrics for their own specific application under consideration. [\dots] This book is written under the seminal auspices that there is no universal method in spherical sampling, being optimal in all aspects. The book presents two essential approaches, namely plane involved sampling (Chapters 6 to 10) and sphere intrinsic sampling (Chapters 11 to 16). The first one fills out the first half of the book and uses tools from a transfer back to the bivariate Euclidean space such as stereographic mapping, Kelvin transform, polar coordinates. The second one takes advantage of the rotational invariance on the sphere and the rotational-invariant cha…
reviewed by: Wolfgang Näther
Mathematics Subject Classification ID: 86-02
Mathematics Subject Classification ID: 94-02
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 62D05
Mathematics Subject Classification ID: 33C55
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 94A20
Mathematics Subject Classification ID: 86A32
Mathematics Subject Classification ID: 86A04
Mathematics Subject Classification ID: 94A08
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 6863919
zbMATH Keywords: spherical harmonics
zbMATH Keywords: pseudodifferential operators
zbMATH Keywords: bandlimited functions
zbMATH Keywords: splines
zbMATH Keywords: wavelets
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-71458-5
OpenAlex ID: W4234438036
description: scientific article; zbMATH DE number 6863919