‎In this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular Sturm-Liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎Also Weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

We nd the adjoint of the Askey-Wilson divided di erence operator with respect to the inner product on L 2 ( 1; 1; (1 x 2 ) 1=2 dx) de ned as a Cauchy principal value and show that the Askey-Wilson polynomials are solutions of a q-Sturm-Liouville problem. From these facts we deduce various properties of the polynomials in a simple and straightforward way. We also provide an operator theoretic de...

The measure algebras of the title are those which are also hypergroups with some regularity conditions, Examples include the convolutions associated with Jacobi polynomial series and Fourier Bessel series, It is shown here that there is a one-to-one correspondence between these hypergroups and a class of Sturm-Liouville problems which have the characters of the hypergroup as eigenfunctions, The...

It is well known that the two spectra {λn} and {μn} uniquely determine the potential function q (r) in a Sturm-Liouville equation defined on the unit interval having the singularity type ( ) 2 1 2 r r + +   (where  is a integer) at the point zero. In this work, we give the solution of the inverse problem on two partially noncoincide spectra for the Sturm-Liouville equation with the peculiari...

We consider the structure of the solution set of a nonlinear SturmLiouville boundary value problem defined on a general time scale. Using global bifurcation theory we show that unbounded continua of non-trivial solutions bifurcate from the trivial solution at the eigenvalues of the linearization, and we show that certain nodal properties of the solutions are preserved along these continua. Thes...

We consider the fourth order boundary value problem (ry′′)′′+(py′)′+ qy = λwy, y(a) = y′(a) = y(b) = y′(b) = 0, which is used in a variety of physical models. For such models, the extremal values of the smallest eigenvalue help answer certain optimization problems, such as maximizing the fundamental frequency of a vibrating elastic system or finding the tallest column that will not buckle under...

Solving inverse scattering problem for a discrete Sturm–Liouville operator with a rapidly decreasing potential one gets reflection coefficients s± and invertible operators I +Hs± , where Hs± is the Hankel operator related to the symbol s±. The Marchenko– Faddeev theorem (in the continuous case) [6] and the Guseinov theorem (in the discrete case) [4], guarantees the uniqueness of solution of the...