The Diversity And Beauty Of Applied Operator Theory
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The Diversity and Beauty of Applied Operator Theory
This book presents 29 invited articles written by participants of the International Workshop on Operator Theory and its Applications held in Chemnitz in 2017. The contributions include both expository essays and original research papers illustrating the diversity and beauty of insights gained by applying operator theory to concrete problems. The topics range from control theory, frame theory, Toeplitz and singular integral operators, Schrödinger, Dirac, and Kortweg-de Vries operators, Fourier integral operator zeta-functions, C*-algebras and Hilbert C*-modules to questions from harmonic analysis, Monte Carlo integration, Fibonacci Hamiltonians, and many more. The book offers researchers in operator theory open problems from applications that might stimulate their work and shows those from various applied fields, such as physics, engineering, or numerical mathematics how to use the potential of operator theory to tackle interesting practical problems.
Operator Theory, Analysis and the State Space Approach
This volume is dedicated to Rien Kaashoek on the occasion of his 80th birthday and celebrates his many contributions to the field of operator theory during more than fifty years. In the first part of the volume, biographical information and personal accounts on the life of Rien Kaashoek are presented. Eighteen research papers by friends and colleagues of Rien Kaashoek are included in the second part. Contributions by J. Agler, Z.A. Lykova, N.J. Young, J.A. Ball, G.J. Groenewald, S. ter Horst, H. Bart, T. Ehrhardt, B. Silbermann, J.M. Bogoya, S.M. Grudsky, I.S. Malysheva, A. Böttcher, E. Wegert, Z. Zhou, Y. Eidelman, I. Haimovici, A.E. Frazho, A.C.M. Ran, B. Fritzsche, B. Kirstein, C.Madler, J. J. Jaftha, D.B. Janse van Rensburg, P. Junghanns, R. Kaiser, J. Nemcova, M. Petreczky, J.H. van Schuppen, L. Plevnik, P. Semrl, A. Sakhnovich, F.-O. Speck, S. Sremac, H.J. Woerdeman, H. Wolkowicz and N. Vasilevski.
Semigroups of Operators – Theory and Applications
This book features selected and peer-reviewed lectures presented at the 3rd Semigroups of Operators: Theory and Applications Conference, held in Kazimierz Dolny, Poland, in October 2018 to mark the 85th birthday of Jan Kisyński. Held every five years, the conference offers a forum for mathematicians using semigroup theory to discover what is happening outside their particular field of research and helps establish new links between various sub-disciplines of semigroup theory, stochastic processes, differential equations and the applied fields. The book is intended for researchers, postgraduate and senior students working in operator theory, partial differential equations, probability and stochastic processes, analytical methods in biology and other natural sciences, optimisation and optimal control. The theory of semigroups of operators is a well-developed branch of functional analysis. Its foundations were laid at the beginning of the 20th century, while Hille and Yosida’s fundamental generation theorem dates back to the forties. The theory was originally designed as a universal language for partial differential equations and stochastic processes but, at the same time, it started to become an independent branch of operator theory. Today, it still has the same distinctive character: it develops rapidly by posing new ‘internal’ questions and, in answering them, discovering new methods that can be used in applications. On the other hand, it is being influenced by questions from PDE’s and stochastic processes as well as from applied sciences such as mathematical biology and optimal control and, as a result, it continually gathers new momentum. However, many results, both from semigroup theory itself and the applied sciences, are phrased in discipline-specific languages and are hardly known to the broader community.