Dr. Ilwoo Cho is a Professor in the Department of Mathematics and Statistics at St. Ambrose University, Davenport, Iowa, USA. He holds a PhD in Mathematics from the University of Iowa. His research is focused in the areas of Free Probability, Operator Theory, Operator Algebra, Noncommutative Dynamical Systems, and Combinatorics. He has contributed chapters to several books, including Methods of Mathematical Modelling and Computation for Complex Systems, Springer; New Directions in Function Theory: From Complex to Hypercomplex to Noncommutative, Birkhäuser; Nonlinear Analysis: Problems, Applications and Computational Methods, Springer; Complex Function Theory, Operator Theory, Schur Analysis and Systems Theory, Birkhäuser; and Mathematical Methods and Modelling in Applied Sciences, Springer. Dr. Hemen Dutta PhD is a Professor at Gauhati University, India. He also served three other higher learning academic institutions in different capacities prior to joining the Gauhati University. His current research interests are in the areas of nonlinear analysis and mathematical modeling. He is a regular and guest editor of several international indexed journals. He has published 25 books, including Mathematical Modelling and Analysis of Infectious Diseases, New Trends in Applied Analysis and Computational Mathematics, Current Trends in Mathematical Analysis and Its Interdisciplinary Applications from Springer, Concise Introduction to Basic Real Analysis, Topics in Contemporary Mathematical Analysis and Applications, and Mathematical Methods in Engineering and Applied Sciences from CRC Press, and Fractional Order Analysis: Theory, Methods and Applications from Wiley, among others. Dr. Dutta is also an honorary research affiliate and speaker for several international and national events.

"The present monograph considers semicircular elements whose free distributions are the semicircular law induced by some mutually orthogonal projections on the free Hilbert space induced by fixed multi Hilbert spaces…. This motivates the authors of the present monograph to introduce certain operators which preserve or distort the semicircular law.... The book will be interesting and useful for mathematicians working in this area." --Ali Talebi, zbMATHOpen

• 1. Fundamentals2. Semicircular Elements Induced by Orthogonal Projections3. Semicircular Elements Induced by Projections On l2-Spaces4. Jump Operators on Free Hilbert Spaces and Deformed Semicircular Laws5. Shift Operators on Free Hilbert Spaces and Deformed Semicircular Laws6. Jump-Shift Operators on Free Hilbert Spaces and Deformed Semicircular Laws

Dr. Ilwoo Cho is a Professor in the Department of Mathematics and Statistics at St. Ambrose University, Davenport, Iowa, USA. He holds a PhD in Mathematics from the University of Iowa. His research is focused in the areas of Free Probability, Operator Theory, Operator Algebra, Noncommutative Dynamical Systems, and Combinatorics. He has contributed chapters to several books, including Methods of Mathematical Modelling and Computation for Complex Systems, Springer; New Directions in Function Theory: From Complex to Hypercomplex to Noncommutative, Birkhäuser; Nonlinear Analysis: Problems, Applications and Computational Methods, Springer; Complex Function Theory, Operator Theory, Schur Analysis and Systems Theory, Birkhäuser; and Mathematical Methods and Modelling in Applied Sciences, Springer. Dr. Hemen Dutta PhD is a Professor at Gauhati University, India. He also served three other higher learning academic institutions in different capacities prior to joining the Gauhati University. His current research interests are in the areas of nonlinear analysis and mathematical modeling. He is a regular and guest editor of several international indexed journals. He has published 25 books, including Mathematical Modelling and Analysis of Infectious Diseases, New Trends in Applied Analysis and Computational Mathematics, Current Trends in Mathematical Analysis and Its Interdisciplinary Applications from Springer, Concise Introduction to Basic Real Analysis, Topics in Contemporary Mathematical Analysis and Applications, and Mathematical Methods in Engineering and Applied Sciences from CRC Press, and Fractional Order Analysis: Theory, Methods and Applications from Wiley, among others. Dr. Dutta is also an honorary research affiliate and speaker for several international and national events.

"The present monograph considers semicircular elements whose free distributions are the semicircular law induced by some mutually orthogonal projections on the free Hilbert space induced by fixed multi Hilbert spaces…. This motivates the authors of the present monograph to introduce certain operators which preserve or distort the semicircular law.... The book will be interesting and useful for mathematicians working in this area." --Ali Talebi, zbMATHOpen

• 1. Fundamentals2. Semicircular Elements Induced by Orthogonal Projections3. Semicircular Elements Induced by Projections On l2-Spaces4. Jump Operators on Free Hilbert Spaces and Deformed Semicircular Laws5. Shift Operators on Free Hilbert Spaces and Deformed Semicircular Laws6. Jump-Shift Operators on Free Hilbert Spaces and Deformed Semicircular Laws

Dr. Ilwoo Cho is a Professor in the Department of Mathematics and Statistics at St. Ambrose University, Davenport, Iowa, USA. He holds a PhD in Mathematics from the University of Iowa. His research is focused in the areas of Free Probability, Operator Theory, Operator Algebra, Noncommutative Dynamical Systems, and Combinatorics. He has contributed chapters to several books, including Methods of Mathematical Modelling and Computation for Complex Systems, Springer; New Directions in Function Theory: From Complex to Hypercomplex to Noncommutative, Birkhäuser; Nonlinear Analysis: Problems, Applications and Computational Methods, Springer; Complex Function Theory, Operator Theory, Schur Analysis and Systems Theory, Birkhäuser; and Mathematical Methods and Modelling in Applied Sciences, Springer. Dr. Hemen Dutta PhD is a Professor at Gauhati University, India. He also served three other higher learning academic institutions in different capacities prior to joining the Gauhati University. His current research interests are in the areas of nonlinear analysis and mathematical modeling. He is a regular and guest editor of several international indexed journals. He has published 25 books, including Mathematical Modelling and Analysis of Infectious Diseases, New Trends in Applied Analysis and Computational Mathematics, Current Trends in Mathematical Analysis and Its Interdisciplinary Applications from Springer, Concise Introduction to Basic Real Analysis, Topics in Contemporary Mathematical Analysis and Applications, and Mathematical Methods in Engineering and Applied Sciences from CRC Press, and Fractional Order Analysis: Theory, Methods and Applications from Wiley, among others. Dr. Dutta is also an honorary research affiliate and speaker for several international and national events.

"The present monograph considers semicircular elements whose free distributions are the semicircular law induced by some mutually orthogonal projections on the free Hilbert space induced by fixed multi Hilbert spaces…. This motivates the authors of the present monograph to introduce certain operators which preserve or distort the semicircular law.... The book will be interesting and useful for mathematicians working in this area." --Ali Talebi, zbMATHOpen

• 1. Fundamentals2. Semicircular Elements Induced by Orthogonal Projections3. Semicircular Elements Induced by Projections On l2-Spaces4. Jump Operators on Free Hilbert Spaces and Deformed Semicircular Laws5. Shift Operators on Free Hilbert Spaces and Deformed Semicircular Laws6. Jump-Shift Operators on Free Hilbert Spaces and Deformed Semicircular Laws