Publications

1. Stability of the concentration inequality on polynomials (with J. Ortega-Cerdà)

Commun. Math. Phys. 406 (2025) 112   arXiv

Keywords: localization operator, Wehrl entropy, quantitative estimates, coherent states.

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

Analysis & PDE 18:8 (2025) 2033-2060   arXiv

Keywords: inverse problem, reconstruction.

3. Classification of exceptional Jacobi polynomials (with D. Gómez-Ullate and R. Milson)

Preprint 2024   arXiv

Keywords: exceptional orthogonal polynomials, Darboux transformations, spectral diagrams.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.

12. 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.

13. 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.

14. 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.

15. 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.

16. 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. 

Expository paper

• The Calderón problem for local and nonlocal Schrödinger equations

Cutting-Edge Mathematics. RSME 2022. RSME Springer Series

Conference paper based in turn on previous works with G. Covi, A. Rülando and W. Zatoń.

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: