Open access peer-reviewed Edited Volume

Operator Theory - Recent Advances, New Perspectives and Applications

Abdo Abou Jaoudé

Notre Dame University - Louaize

Abdo Abou Jaoudé is a pioneering Associate Professor of Mathematics and Statistics at Notre Dame University-Louaizé. He holds two PhDs in Mathematics and Prognostics from the Lebanese University and Aix-Marseille University. His research interests are in the field of mathematics.

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Linear Operators Normal Operators Spectral Theorem Applications Differential Operators Integral Operators Functional Calculus Complex Variables Complex Analysis Theory Recent Advances Latest Trends

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About the book

In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operators or closed operators and consideration may be given to nonlinear operators. The study, which depends heavily on the topology of function spaces, is a branch of functional analysis. If a collection of operators forms an algebra over a field, then it is an operator algebra. The description of operator algebras is part of operator theory. Single operator theory deals with the properties and classification of operators, considered one at a time. For example, the classification of normal operators in terms of their spectra falls into this category.

The theory of operator algebras brings algebras of operators such as C*-algebras to the fore. Many operators that are studied are operators on Hilbert spaces of holomorphic functions, and the study of the operator is intimately linked to questions in function theory. For example, Beurling's theorem describes the invariant subspaces of the unilateral shift in terms of inner functions, which are bounded holomorphic functions on the unit disk with unimodular boundary values almost everywhere on the circle. Beurling interpreted the unilateral shift as multiplication by the independent variable on the Hardy space. The success in studying multiplication operators, and more generally Toeplitz operators (which are multiplication, followed by projection onto the Hardy space) has inspired the study of similar questions in other spaces, such as the Bergman space. Hence, operator theory has a connection with complex analysis. Additionally, this book will be intended to be an illustration of the use of operator theory when applied to solve specific problems in pure and applied mathematics, engineering, physics, or science in general.
 

Publishing process

Book initiated and editor appointed

Date completed: April 13th 2022

Applications to edit the book are assessed and a suitable editor is selected, at which point the process begins.

Chapter proposals submitted and reviewed

Deadline Extended: Open for Submissions

Potential authors submit chapter proposals ready for review by the academic editor and our publishing review team.

Approved chapters written in full and submitted

Deadline for full chapters: July 10th 2022

Once approved by the academic editor and publishing review team, chapters are written and submitted according to pre-agreed parameters

Full chapters peer reviewed

Review results due: September 28th 2022

Full chapter manuscripts are screened for plagiarism and undergo a Main Editor Peer Review. Results are sent to authors within 30 days of submission, with suggestions for rounds of revisions.

Book compiled, published and promoted

Expected publication date: November 27th 2022

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About the editor

Abdo Abou Jaoudé

Notre Dame University - Louaize

Abdo Abou Jaoudé has been teaching for many years and has a passion for researching and teaching mathematics. He is currently an Associate Professor of Mathematics and Statistics at Notre Dame University-Louaizé (NDU), Lebanon. He holds a BSc and an MSc in Computer Science from NDU, and three PhDs in Applied Mathematics, Computer Science, and Applied Statistics and Probability, all from Bircham International University through a distance learning program. He also holds two PhDs in Mathematics and Prognostics from the Lebanese University, Lebanon, and Aix-Marseille University, France. Dr. Abou Jaoudé's broad research interests are in the field of applied mathematics. He has published twenty-three international journal articles and six contributions to conference proceedings, in addition to seven books on prognostics, pure and applied mathematics, and computer science.

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Book chapters authored 4

Books edited 2

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