Functional Calculus: Theory and Applications

Functional calculus is a mathematical framework used to extend the concept of functions of a real variable to functions of operators. This approach is particularly useful in functional analysis and operator theory. In essence, it allows the application of algebraic operations and functions, such as polynomials or exponentials, to operators on a Hilbert space or Banach space. Functional calculus plays a crucial role in quantum mechanics, spectral theory, and differential equations, where operators often represent physical observables or evolution processes. The most common forms are the polynomial functional calculus and the more advanced holomorphic functional calculus. These tools enable the analysis and manipulation of operator functions, facilitating solutions to complex mathematical and physical problems by extending familiar concepts of functions to an operator setting. This book provides comprehensive insights into the field of functional calculus. It presents the complex subject of functional calculus in the most comprehensible and easy to understand language. Students, researchers, experts and all associated with mathematics will benefit alike from this book.