This volume presents selected contributions from a conference held at Chapman University in January 2024 on Schur analysis and its applications. The papers, written by leading researchers in the field, are divided into four sections: function theory, harmonic analysis, and operator theory; Schur analysis and signal processing; hypercomplex analysis; and infinite dimensional analysis, probabilities, and non-commutative theory. The volume will be a valuable resource for mathematicians and other researchers interested in learning about the latest developments and applications of Schur analysis.

Presents the latest research in the rapidly developing field of Schur analysis Explores applications in signal processing, neural networks, linear systems, and mathematical physics Features contributions written by experts in their areas

Autorentext

Daniel Alpay was born in Paris, France and has a double formation of electrical engineer (Telecom Paris) and theoretical mathematics (Weizmann Institute, Rehovot, Israel). His research interests lie in hypercomplex analysis, operator theory, stochastic processes (in particular in the setting of infinite dimensional analysis), and mathematical physics. He has written a number of research books and more than 310 papers. Building on his research, he wrote three exercises books, two of them on complex analysis. He was a chaired professor at Ben-Gurion University  (Beer-Sheva, Israel) and is now Professor at Chapman University (Orange, California), where he holds the Foster G. and Mary McGaw Professorship in Mathematical Sciences.

Adrian Vajiac's interests include the geometry and invariants of 4-manifolds, mathematical physics, topological quantum field theories, and hypercomplex analysis. He wrote two books and several papers in these directions and is now Co-Director of the Computational and Data Science Program at Chapman University, Orange, CA.

Mihaela Vajiac was born in Targoviste, Romania, and completed magna cum laude both her undergraduate degree at the University of Bucharest and her PhD at Boston University. Her research interests include Symplectic Geometry, Integrable Systems, and Hypercomplex Analysis, and she has been a co-editor to five similar volumes. She is now Director of the Center of Complex and Hypercomplex Analysis and Program Director of Mathematics at Chapman University, Orange, CA.

Inhalt

Preface.- Continuous Stochastic Linear Systems: A white noise space approach.- Models for q-commuting and doubly q-commuting pairs of isometries.- Operator orbit Frames and frame-like Fourier expansions.- The q-Dirac Operator on Quantum Euclidean Space.- On the modified hyperholomorphic Dirichlet space on the punctured unit ball.- Linear Operators On a System H of All Scaled Hypercomplex Numbers.- Vertex-Glued Connected Finite Graphs and Mutually Free Semicircular Elements.- Extreme Points of Infinite-dimensional Symmetric Doubly Stochastic Matrices.- The Weyl sets corresponding to matricial Ham- burger and Stieltjes moment problems.- Geometry of the slice regular M obius transformations of the quaternionic unit ball.- Hypertwined Regularity in SplitQuaternionic Analysis.- Applications of Multihyperbolic Analysis.