Hilbert Spaces: Properties and Applications


Le Bin Ho (Editor)
Department of Physics, Kindai University, Osaka, Japan

Series: Mathematics Research Developments

This collective book presents selected topics in the modern research of Hilbert space. Throughout this book, various mathematical properties of the Hilbert space and extended Hilbert space are given, accompanied by reliable solutions and exciting applications to scientific and engineering problems. It first provides some general viewpoints on convex sets, projections, and orthogonality in Hilbert spaces and then focuses on the mild solutions, the stability, and the controllability of various classes of differential equations in Hilbert spaces and applications. It also is devoted to a discussion of the extended Hilbert space, including the hypercomplex Hilbert space, the Bargmann-Hilbert space, and the enlarged Hilbert space where various mathematical and physical applications are given. A reduced Hilbert space for model Hamiltonians is also given. Together, the book presents to readers a picture of the modern theory of Hilbert space in its complexness and usefulness. The book is accessible for graduate students and could be served as a reference for scholars.
(Imprint: Nova)

Table of Contents

Table of Contents


Chapter 1. Some Considerations on Orthogonality, Strict Separation Theorems and Applications in Hilbert Spaces
(Manuel Alberto M. Ferreira, Instituto Universitário de Lisboa, Information Sciences, Technologies and Architecture Research Center, Business Research Unit, Lisboa, Portugal)

Chapter 2. Solution Estimates for Autonomous Differential Equations in a Hilbert Space with Several Delays
(Michael Gil, Department of Mathematics, Ben Gurion University of the Negev, Beer-Sheva, Israel)

Chapter 3. Controllability of Quasi-Linear Evolution Differential System in a Separable Banach Space
(Bheeman Radhakrishnan, Department of Mathematics, PSG College of Technology, Coimbatore, TamilNadu, India)

Chapter 4. Derivations of Operator Algebras on Hypercomplex Hilbert Spaces and Related Modules
(S.V. Ludkowski, Department of Applied Mathematics, Moscow State Technological University MIREA-RTU, Moscow, Russia)

Chapter 5. On Analytic Solutions of the Driven, 2-Photon and Two-Mode Quantum Rabi Models
(Yao-Zhong Zhang, School of Mathematics and Physics, University of Queensland, Brisbane, Queensland, Australia)

Chapter 6. Hilbert Space of Model Hamiltonians
(Medha Sharma, PhD, Mater Dei School,Tilak Lane, New Delhi, India)

Chapter 7. Enlarged Hilbert Spaces and Applications in Quantum Physics
(Le Bin Ho, Department of Physics, Kindai University, Higashi-Osaka, Japan, and others)



“The text is remarkable both from a scientific and pedagogical point of view. It is organized in such a way that the first chapters form the basis for the following, linked together as if it were a construction that is based on the foundations and evolves to the roof.” READ MORE… – Manuel Alberto M. Ferreira, Professor Emeritus, ISCTE – Lisbon University Institute, Lisbon, Portugal

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