Multiscale Methods for Fredholm Integral Equations

Author: Zhongying Chen
Publisher: Cambridge University Press
ISBN: 9781107103474
Release Date: 2015-07-16
Genre: Mathematics

Presents the state of the art in the study of fast multiscale methods for solving these equations based on wavelets.

Generalized Mercer Kernels and Reproducing Kernel Banach Spaces

Author: Yuesheng Xu
Publisher: American Mathematical Soc.
ISBN: 9781470435509
Release Date: 2019-04-10
Genre: Banach spaces

This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation. First the authors verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and universal approximation. Then, they develop a new concept of generalized Mercer kernels to construct p-norm RKBSs for 1≤p≤∞ .

Volterra Integral Equations

Author: Hermann Brunner
Publisher: Cambridge University Press
ISBN: 9781316982655
Release Date: 2017-01-20
Genre: Mathematics

This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels, and VIEs with non-compact operators. It will act as a 'stepping stone' to the literature on the advanced theory of VIEs, bringing the reader to the current state of the art in the theory. Each chapter contains a large number of exercises, extending from routine problems illustrating or complementing the theory to challenging open research problems. The increasingly important role of VIEs in the mathematical modelling of phenomena where memory effects play a key role is illustrated with some 30 concrete examples, and the notes at the end of each chapter feature complementary references as a guide to further reading.

Collected papers

Author: Wolfgang Krull
Publisher: Walter de Gruyter
ISBN: 3110127717
Release Date: 1999-01
Genre: Mathematics

Wolfgang Krull (1899-1971) is famous for his contributions to the area of maths now known as abstract commutative algebra. These two volumes contain all his papers published in mathematical periodicals. Volume 1 covers the period 1921 to 1938, Volume 2 covers the period 1939 to 1973.