First-rate mathematicians as contributing authors Covers most recent achievements in the area as well as state-of-the-art expositions Different aspects of hypercomplex analysis Includes supplementary material: sn. pub/extras
Focusing on quaternionic analysis, this book explores extensions of key approximation results from complex analysis. It highlights significant inequalities related to the derivatives of polynomials with quaternionic coefficients. Most of the content stems from the authors' recent research on approximating slice regular functions of a quaternionic variable, offering valuable insights into this advanced mathematical field.
Focusing on quaternionic linear operators, this work explores their unique properties compared to complex operators, particularly in the noncommutative realm. It introduces concepts like the S-spectrum and S-resolvent operators while examining de Branges spaces, which serve as quaternionic analogs of analytic function spaces. The study emphasizes specific reproducing kernels in the unit ball or half-space of quaternions, delving into Hilbert, Pontryagin, and Krein spaces and their connections to operator models.
This book explores Clifford algebras and their applications in mathematical physics, numerical analysis, and computer science, focusing on linear partial differential equations and Dirac systems. It emphasizes computational techniques and requires knowledge of various mathematical fields, making it suitable for graduate students and researchers.
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 The book includes previously unpublished results and provides the basis for new directions of research.
* Original articles and survey articles in honor of the sixtieth birthday of Carlos A. Berenstein reflect his diverse research interests from interpolation to residue theory to deconvolution and its applications to issues ranging from optics to the study of blood flow * Contains both theoretical papers in harmonic and complex analysis, as well as more applied work in signal processing * Top-notch contributors in their respective fields