Publications

1. Reconstruction for the Calderón problem with Lipschitz conductivities (with P. Caro and K.M. Rogers)

Preprint    arXiv

Keywords: inverse problem, reconstruction.

2. On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols (with G. Covi and A. Rüland)

J. Differ. Equ. 341  (2022)  79-149    arXiv

Keywords: inverse problem, nonlocal operators, directional antilocality.

3. Exceptional Gegenbauer polynomials via isospectral deformation   (with D. Gómez-Ullate, R. Milson and J. Munday)

Stud. Appl. Math. 149:2 (2022) 324-363    arXiv

Keywords: exceptional orthogonal polynomials, Darboux transformations, isospectral deformations.

4. Runge approximation and stability improvement for a partial data Calderón problem for the acoustic Helmholtz equation (with A. Rüland and W. Zatoń)

Inverse Probl. Imaging 16:1 (2022) 251–281    arXiv

Keywords:  Runge approximation, quantitative unique continuation, partial data inverse problem, stability estimates, high frequency limit.

5. Exceptional Legendre polynomials and confluent Darboux transformations   (with D. Gómez-Ullate and R. Milson)

Symmetry Integr. Geom. 17 (2021) 016   arXiv

Keywords: exceptional orthogonal polynomials, Darboux transformations, isospectral deformations.

6. On Two Methods for Quantitative Unique Continuation Results for Some Nonlocal Operators   (with A. Rüland)

Commun. Part. Diff. Eq. 45:11 (2020) 1512-1560   arXiv 

Keywords: nonlocal operators, unique continuation, logarithmic stability, moment problem.

7. Strong unique continuation for the higher order fractional Laplacian   (with A. Rüland)

Mathematics in Engineering 1 (2019) 715-774   arXiv

Keywords: unique continuation, fractional Schrödinger equation, higher order nonlocal operators, Carleman estimates.

8. Approximation theorems for parabolic equations and movement of local hot spots   (with A. Enciso and D. Peralta-Salas)

Duke Math. J. 168 (2019) 897-939   arXiv

Keywords: global approximation theorems, hot spots, nodal sets, parabolic equations.

9. A Bochner type characterization for exceptional orthogonal polynomials   (with D. Gómez-Ullate and R. Milson)

J. Math. Anal. Appl. 472 (2019) 584-626   arXiv  

Keywords: exceptional orthogonal polynomials, Darboux transformations, Sturm–Liouville problems, trivial monodromy.

10. The Biot-Savart operator of a bounded domain   (with A. Enciso and D. Peralta-Salas)

J. Math. Pures Appl.,  119 (2018) 85-113   arXiv

Keywords: Biot–Savart law, boundary value problems for curl, integral kernel.

11. Minimal graphs with micro-oscillations   (with A. Enciso and D. Peralta-Salas)

J. Differ. Equ. 265 (2018) 3339-3344   arXiv

Keywords: minimal surfaces, level sets, approximation theorems.

12. Shannon entropy and particle decays   (with P. Carrasco Millán, F.J. Llanes-Estrada, A. Porras Riojano and E.M. Sánchez García) 

Nucl. Phys. B 930 (2018) 583-596   arXiv      

Keywords: Shannon's information entropy, hadron decay chanels.

13. Oscillation theorems for the Wronskian of an arbitrary sequence of eigenfunctions of Schrödinger's equation   (with D. Gómez-Ullate)

Lett. Math. Phys. 10 5(2015), 551-573   arXiv

Keywords: Sturm–Liouville problems, Wronskian determinants, classical and exceptional orthogonal polynomials, counting zeros.

14. The Infinite Square Well with Point Interaction: A Discussion on the Different Parametrizations   (with M. Gadella, S. González-Martín and F.H. Maldonado-Villamizar) 

Int. J. Theor. Phys. 53 (2014), 1614-1627   arXiv

Keywords: point potentials, self-adjoint extensions. 

PhD Thesis:  Global approximation theorems for partial differential equations and applications slides

❅ You can find slides of talks about some of the previous publications here.

❅ Publications can also be consulted in the following research profiles: