Some new properties of hilbert quasilinear spaces

The thesis titled "Some New Properties of Hilbert Quasilinear Spaces" consists of four chapters. The first chapter provides information about the topics covered in the thesis and explains the procedures to be carried out in the subsequent chapters. In the second chapter, fundamental concepts, definitions, and theorems used in the thesis are presented. The third chapter defines quasilinear spaces, which generalize linear spaces, and explains algebraic expressions corresponding to linear spaces. The fourth chapter focuses on spaces formed by interval-valued functions in L₂([a,b],I_{R}). It presents definitions and theorems concerning these spaces. Additionally, a method is proposed for calculating the energies of incomplete information non-deterministic signals, and the deterministic autocorrelation method is explained for measuring error between these signals. In this context, Hilbert quasilinear space is utilized.