TY  - BOOK
AU  - Samer Derhem Hussein Makharesh
AU  - Alaa Eldeen Hamza , 
AU  - Mahmoud Annaby , 
TI  - On Sturm-Liouville theory for Hahn difference operator / 
PY  - 2016///
CY  - Cairo : 
PB  - Samer Derhem Hussein Makharesh , 
KW  - Hahn Difference operator
KW  - q-difference operator
KW  - Sturm-Liouville theory
N1  - Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics; Issued also as CD
N2  - This thesis introduces a comprehensive study for Sturm-Liouville theory of the q,{u019C}-Hahn difference operators in the regular setting. We define a hilbert space of q,{u019C}-square summable functions in terms of Jackson-Nörlund integral. The formulation of the self-adjoint operator and the properties of the eigenvalues and the eigenfunctions are discussed. The construction of green{u2019}s function is developed and study for q,{u019C}-fredholem integral operator is established. Hence, an eigenfunctions expansion theorem is derived and illustrative examples are exhibited. We also introduce a numerical simulations and illustrations. We give some comparisons between trigonometric functions and the q,{u019C}-counterparts. We also test numerically the asymptotic behaviour of the zeros of q,{u019C}-trigonometric functions. The numerical experiments precisely reflects the theoretical results with this respect
UR  - http://172.23.153.220/th.pdf
ER  -