Theory Of Inverse Operators In Functional Analysis: Fundamental Theorems And Practical Applications
Keywords:
Inverse operator, Banach space, injectivity, surjectivity, invertibilityAbstract
This article analyzes one of the central concepts of functional analysis—the theory of inverse operators and their properties in linear spaces. Within the scope of this research, the conditions for operator invertibility, Banach’s Bounded Inverse Theorem, and Jacques Hadamard’s concept of ill-posed problems are examined. The primary objective of this paper is to bridge the gap between pure mathematical abstraction and its critical role in applied fields such as medical imaging (computed tomography) and geophysics (seismic inverse problems).
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Funksional analizdan masalalar to‘plami: II qism / J. Abdullayev, R. G‘anixo‘jayev, I. Ikromov. - Samarqand: Turon-Iqbol, 2012.-150 b.
