On the Lipschitz stability of inverse nodal problem for Dirac system

Emrah YILMAZ; Hikmet KEMALOĞLU

doi:https://doi.org/10.31801/cfsuasmas.733215

Article Details

On the Lipschitz stability of inverse nodal problem for Dirac system

Authors:

Emrah YILMAZ | Hikmet KEMALOĞLU

Publisher:

Ankara University

Main Topics:

Probabilities & applied mathematics

Journal:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 2021 Vol.70 Issue 1, pp.341-356

Document Type:

Article

Publication Date:

6/2021

Document Language:

English

Document ID (Org No.):

2000908996

Frequency:

Quarterly

eISSN:

2618-6470

pISSN:

1303-5991

DOI:

https://doi.org/10.31801/cfsuasmas.733215

Abstract:

 

Inverse nodal problem on Dirac operator is determination problem of the parameters in the boundary conditions, number m and potential function V 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 the space of all V functions is homeomorphic to the partition set of all space of asymptotically equivalent nodal sequences induced by an equivalence relation. Moreover, 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 eigenfunction. Our technique depends on the explicit asymptotic expressions of the nodal parameters and, it is basically similar to [1, 2] which is given for Sturm-Liouville and Hill's operators, respectively.

Article Details

On the Lipschitz stability of inverse nodal problem for Dirac system

Authors: Emrah YILMAZ | Hikmet KEMALOĞLU

Publisher: Ankara University

Main Topics: Probabilities & applied mathematics

Journal: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 2021 Vol.70 Issue 1, pp.341-356

Document Type: Article

Publication Date: 6/2021

Document Language: English

Document ID (Org No.): 2000908996

Frequency: Quarterly

eISSN: 2618-6470

pISSN: 1303-5991

DOI: https://doi.org/10.31801/cfsuasmas.733215

Issues

Authors:

Emrah YILMAZ | Hikmet KEMALOĞLU

Publisher:

Ankara University

Main Topics:

Probabilities & applied mathematics

Journal:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 2021 Vol.70 Issue 1, pp.341-356

Document Type:

Article

Publication Date:

6/2021

Document Language:

English

Document ID (Org No.):

2000908996

Frequency:

Quarterly

eISSN:

2618-6470

pISSN:

1303-5991

DOI:

https://doi.org/10.31801/cfsuasmas.733215