This thesis focuses on the fundamental problem of characterising partially coherent beams. The book describes several non-interferometric methods based on phase-space tomography for recovering the spatial coherence information of optical beams. In the context of optical beams, partially coherent light provides numerous advantages over coherent light. From microscopy to optical communications, …
This Springer Brief investigates spectrum sharing with limited channel feedback in various cognitive radio systems, such as point-to-point, broadcast scheduling and ad-hoc networks. The design aim is to optimally allocate the secondary resources to improve the throughput of secondary users while maintaining a certain quality of service for primary users. The analytical results of optimal resour…
Optical coherence tomography (OCT) is the optical analog of ultrasound imaging and is a powerful imaging technique that enables non-invasive, in vivo, high resolution, cross-sectional imaging in biological tissue. Between 30 to 40 Million OCT imaging procedures are performed per year in ophthalmology. The overall market is estimated at more than 0.5 Billion USD. A new generation OCT technology…
This volume collects a selected number of papers presented at the International Workshop on Operator Theory and its Applications (IWOTA) held in July 2014 at Vrije Universiteit in Amsterdam. Main developments in the broad area of operator theory are covered, with special emphasis on applications to science and engineering. The volume also presents papers dedicated to the eightieth birthday of D…
This book collects the proceedings of the 2012 Abel Symposium, held at the Norwegian Academy of Science and Letters, Oslo. The Symposium, and this book, are focused on two important fields of modern mathematical analysis: operator-related function theory and time-frequency analysis; and the profound interplay between them. Among the original contributions and overview lectures gathered here …
A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and theoretical. There are deep connections with complex analysis, functional analysis…
This book provides a comprehensive tutorial on similarity operators. The authors systematically survey the set of similarity operators, primarily focusing on their semantics, while also touching upon mechanisms for processing them effectively. The book starts off by providing introductory material on similarity search systems, highlighting the central role of similarity operators in such sys…
Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern foundation for introductory courses on ergodic theory, especially for students or researchers with an interest in functional analysis. Whi…
The primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable Hilbert space. The book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. It discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras. The book also introduces the …
This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and…