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Slice Hyperholomorphic Schur Analysis

Author : Daniel Alpay
ISBN : 9783319425146
Genre : Mathematics
File Size : 50.49 MB
Format : PDF
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This book defines and examines the counterpart of Schur functions and Schur analysis in the slice hyperholomorphic setting. It is organized into three parts: the first introduces readers to classical Schur analysis, while the second offers background material on quaternions, slice hyperholomorphic functions, and quaternionic functional analysis. The third part represents the core of the book and explores quaternionic Schur analysis and its various applications. The book includes previously unpublished results and provides the basis for new directions of research.
Category: Mathematics

Recent Applications Of Harmonic Analysis To Function Spaces Differential Equations And Data Science

Author : Isaac Pesenson
ISBN : 9783319555560
Genre : Mathematics
File Size : 32.78 MB
Format : PDF
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The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.
Category: Mathematics

Basics Of Functional Analysis With Bicomplex Scalars And Bicomplex Schur Analysis

Author : Daniel Alpay
ISBN : 9783319051109
Genre : Mathematics
File Size : 39.42 MB
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This book provides the foundations for a rigorous theory of functional analysis with bicomplex scalars. It begins with a detailed study of bicomplex and hyperbolic numbers and then defines the notion of bicomplex modules. After introducing a number of norms and inner products on such modules (some of which appear in this volume for the first time), the authors develop the theory of linear functionals and linear operators on bicomplex modules. All of this may serve for many different developments, just like the usual functional analysis with complex scalars and in this book it serves as the foundational material for the construction and study of a bicomplex version of the well known Schur analysis.
Category: Mathematics

Recent Advances In Inverse Scattering Schur Analysis And Stochastic Processes

Author : Daniel Alpay
ISBN : 9783319103358
Genre : Mathematics
File Size : 83.55 MB
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The volume is dedicated to Lev Sakhnovich, who made fundamental contributions in operator theory and related topics. Besides bibliographic material, it includes a number of selected papers related to Lev Sakhnovich's research interests. The papers are related to operator identities, moment problems, random matrices and linear stochastic systems.
Category: Mathematics

Mathematical Reviews

Author :
ISBN : UOM:39015076649881
Genre : Mathematics
File Size : 52.35 MB
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Category: Mathematics

Banach Algebra Techniques In Operator Theory

Author : Ronald G. Douglas
ISBN : 9781461216568
Genre : Mathematics
File Size : 65.64 MB
Format : PDF, Kindle
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A discussion of certain advanced topics in operator theory, providing the necessary background while assuming only standard senior-first year graduate courses in general topology, measure theory, and algebra. Each chapter ends with source notes which suggest additional reading along with comments on who proved what and when, followed by a large number of problems of varying difficulty. This new edition will appeal to a whole new generation of students seeking an introduction to this topic.
Category: Mathematics