This is the second book of two volumes dedicated to C. F. Gauss on the occasion of his 250th birthday. The objective of the two books is to demonstrate that the heritage of Gauss still has much to offer today in building a strong scientific bridge between mathematics and geoscience.

Volume 2 demonstrates that multidimensional alternating series become more tractable through convergence criteria relating oscillatory properties to an appropriate choice of a Helmholtz operator. As a consequence, new classes of lattice point identities within Shannon sampling can be developed. Wavelet sampling framework is applied to inverse antenna theory. A distinctive feature of sampling is that the coefficients governing the reproduction process for generalized measurements can be determined explicitly using methods originating from lattice point theory. Thus, Volume 2 can be regarded as a forward-looking compendium for addressing ill-posed inverse problems through sampling-based regularization.

This book will be valuable to a broad audience, including mathematicians working in number theory and applied mathematics, as well as professionals in the geosciences, such as geophysics and geoengineering.

Willi Freeden completed his studies in mathematics, geography, and philosophy at the RWTH Aachen University. In 1971, he obtained his Diploma in Mathematics, in 1972, his Staatsexamen in mathematics and geography, in 1975, his PhD in mathematics, and in 1979, his Habilitation. In 1981/1982, he was a visiting research professor at the Ohio State University, Columbus (Department of Geodetic Science and Surveying). He became a professor of mathematics at the RWTH Aachen University (Institute of Pure and Applied Mathematics) in 1984 and later in 1989, joined the University of Kaiserslautern as a professor of technomathematics (Industrial Mathematics). He was appointed and has been the Head of the Geomathematics Group since 1994 and he was the Vice President for Research and Technology at the University of Kaiserslautern, a position he held from 2002 to 2006.