COMPOSITION OPERATORS ON FUNCTION SPACES

Abstract

This thesis investigates the complex relationship between composition operators and function spaces, attempting to understand their behaviour, properties, and practical applications. Composition operators are useful tools in a variety of mathematical disciplines, including functional analysis and operator theory. The paper looks at the theoretical foundations of composition operators, examining their impact on various function space structures such as Banach and Hilbert spaces. The emphasis is on understanding how composition operators alter the properties and characteristics of these function spaces. Furthermore, this study investigates the practical implications of composition operators in signal processing, control theory, and approximation theory. This thesis gives useful insights into the uses of composition operators in several scientific and technical disciplines by investigating their effectiveness in tackling real-world situations. This thesis advances our understanding of composition operators in function spaces through rigorous analysis and investigation, setting the path for future research and applications in a variety of mathematical and scientific disciplines.