Inverse Eigenvalue Problems

This book consists of invited survey articles and research papers in the scientific areas of the “International Workshop on Operator Algebras, Operator Theory and Applications,” which was held in Lisbon in July 2016. Reflecting recent developments in the field of algebras of operators, operator theory and matrix theory, it particularly focuses on groupoid algebras and Fredholm conditions, algebras of approximation sequences, C* algebras of convolution type operators, index theorems, spectrum and numerical range of operators, extreme supercharacters of infinite groups, quantum dynamics and operator algebras, and inverse eigenvalue problems.

The present book contains the 20 articles accepted and published in the Special Issue "Computational Methods and Applications for Numerical Analysis" of the MDPI "Mathematics" journal, which surround the theory, algorithms, programming, software, numerical simulation, and/or novel applications of computational methods to solve problems in engineering, science, and other disciplines related to computations. These topics include finite element methods, finite difference methods, meshless/meshfree methods, physics-informed neural networks, interpolation, approximation, optimization, numerical methods for ordinary/partial differential equations, etc. Their applications include crack propagation, acoustic analysis, elastodynamic analysis, free vibration analysis, structure and topology optimization, fractional equations, eigenvalue problems, inverse problems, etc.

The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to geometry, analysis, physics, and engineering. Divided into five parts, the book's first section is devoted to Clifford analysis; here, topics encompass the Morera problem, inverse scattering associated with the Schrödinger equation, discrete Stokes equations in the plane, a symmetric functional calculus, Poincaré series, differential operators in Lipschitz domains, Paley-Wiener theorems and Shannon sampling, Bergman projections, and quaternionic calculus for a class of boundary value problems.