arXiv subjects

Emrah Yilmaz

Publications and source records attributed to Emrah Yilmaz.

3 recordsLinked to original sources

arXiv2020

On the Lipschitz stability of inverse nodal problem for dirac equation

Inverse nodal problem on Dirac operator is finding the parameters in the boundary conditions, the number m and the potential function V in the Dirac equations by using a set of nodal points of a component of two component vector eigenfunctions as the given spectral data. In this study, we solve a stability problem using nodal set of vector eigenfunctions and show that space of all V functions is homeomorphic to the partition set of all space of asymptotically equivalent nodal sequences induced by an equivalence relation. Furthermore, we give a reconstruction formula for the potential function as a limit of a sequence of functions and associated nodal data of one component of vector eigenfunctions. Our method depends on the explicit asymptotic expressions of the nodal points and nodal lengths and basically, this method is similar to [1, 2] which is given for Sturm-Liouville and Hill operators, respectively.

math.SP↗

arXiv2016

Ambarzumyan Type Theorem for a matrix quadratic Sturm-Liouville equation with energy dependent

Ambarzumyan's theorem for quadratic Sturm-Liouville problem is extended to second order differential systems of dimension d. It is shown that if the spectrum is the same as the spectrum belonging to the zero potential, then the matrix valued functions p and q are both zero

math.SP↗

arXiv2013

Stability of inverse nodal problem for energy-dependent sturm liouville equation

Inverse nodal problem on diffusion operator is the problem of finding the potential functions and parameters in the boundary conditions by using nodal data. In particular, we solve the reconstruction and stability problems using nodal set of eigenfunctions. Furthermore, we show that the space of all potential functions q is homeomorphic to the partition set of all asymptotically equivalent nodal sequences induced by an equivalence relation. To show this stability which is known Lipschitz stability, we have to construct two metric spaces and a map Φ_{dif} between these spaces. We find that Φ_{dif} is a homeomorphism when the corresponding metrics are magnified by the derivatives of q. Basically, this method is similar to Tsay and Cheng which is given for Sturm-Liouville and Hill operators, respectively and depends on the explicit asymptotic expansions of nodal points and nodal lengths.

math.SP↗