Spectral analysis of bessel operator

II SUMMARY Masters Thesis SPECTRAL ANALIYSIS OF BESSEL OPERATOR Hikmet KOYUNBAKAN Fırat University Graduate School of Science and Technology Department of Mathematics 1998, Page: 43 This study is arranged in five chapters. In the first chapter, some fundemental definition and theorems that use often in Spectral theory of Differential operators are given. In the second chapter, General Sturm - Liouville, Bessel equations and Solutions of these equations are examined. In the third chapter, Sturm 's Comparison and Oscillation theorems are proved for Bessel operator. We noted that These theorems are proved for Sturm - Liouville equations by B. M., Levitan. In the fourth chapter, Asymptotic forms are found for eigenvalues, eigenfunctions, normalized numbers, ortonormalized eigenfunctions of Bessel operator. Fifth chapter has constituted original part of the thesis. In this chapter, We investigated of the Euler - Poisson - Darboux equation solution by Riemann methods and existence of translation operator for the Bessel equation with considering the initial value y(0) = 0. KEY WORDS: Eigenvalues, Eigenfunctions, Singularity, Oscillation Theorem, Asymptotic Form, Translation Operator, Riemann ' s Method.