# Mathematics

## List of Publications PDF

- Submitted
- Accepted
- Proceedings
- Theses
- Others

### Submitted

1. E. Blåsten, P. Exner, H. Isozaki, M. Lassas, J. Lu, Inverse problems for locally perturbed lattices — Discrete Hamiltonian and quantum graph. arXiv:2202.00944

### Accepted in Peer-Reviewed Journals

1. E.L.K. Blåsten, L. Päivärinta, S. Sadique, The Fourier, Hilbert and Mellin Transforms on a Half–Line. SIAM Journal of Mathematical Analysis 55, 6 (2023), 7529–7548. doi:10.1137/23m1560628 arXiv:2302.03521
2. E. Blåsten, H. Isozaki, M. Lassas, J. Lu, Inverse Problems for Discrete Heat Equations and Random Walks for a Class of Graphs. SIAM Journal on Discrete Mathematics, 37, 2 (2023), 831–863. doi:10.1137/21m1439936 arXiv:2107.00494
3. E. Blåsten, H. Isozaki, M. Lassas, J. Lu, The Gel'fand's inverse problem for the graph Laplacian. Journal of Spectral Theory, 13, 1 (2023), 1–45. doi:10.4171/jst/455 arXiv:2101.10026
4. E.L.K. Blåsten, V. Pohjola, Cones With Convoluted Geometry That Always Scatter Or Radiate. Inverse Problems, 38, 12 (2022), 125001. doi:10.1088/1361-6420/ac963c arXiv:2110.06044
5. E.L.K. Blåsten, H. Liu, Scattering by curvatures, radiationless sources, transmission eigenfunctions and inverse scattering problems. SIAM Journal on Mathematical Analysis, 53, 4 (2021), 3801–3837. doi:10.1137/20m1384002 arXiv:1808.01425
6. E. Blåsten, H. Liu, J. Xiao, On an electromagnetic problem in a corner and its applications. Analysis & PDE, 14, 7 (2021), 2207–2224. doi:10.2140/apde.2021.14.2207 arXiv:1901.00581
7. E.L.K. Blåsten, H. Liu, On corners scattering stably and stable shape determination by a single far-field pattern. Indiana University Mathematics Journal, 70, 3 (2021), 907–947. doi:10.1512/iumj.2021.70.8411 arXiv:1611.03647
8. E. Blåsten, L. Päivärinta, S. Sadique, Unique Determination of the Shape of a Scattering Screen from a Passive Measurement. Mathematics, 8, 7 (2020), 1156. doi:10.3390/math8071156 arXiv:2006.06546
9. E. Blåsten, H. Liu, Recovering piecewise constant refractive indices by a single far-field pattern. Inverse Problems, 36, 8 (2020), 085005. doi:10.1088/1361-6420/ab958f arxiv:1705.00815
10. E. Blåsten, E. Vesalainen, Non-Scattering Energies and Transmission Eigenvalues in Hn. Annales Academiæ Scientiarum Fennicæ Mathematica, 45, 1 (2020), 547–576. doi:10.5186/aasfm.2020.4522 arXiv:1809.04426
11. E. Blåsten, H. Li, H. Liu, Y. Wang, Localization and geometrization in plasmon resonances and geometric structures of Neumann-Poincaré eigenfunctions. ESAIM: Mathematical Modelling and Numerical Analysis, 54, 3 (2020), 957–976. doi:10.1051/m2an/2019091 arXiv:1809.08533
12. E. Blåsten, L. Tzou, J. Wang, Uniqueness for the inverse boundary value problem with singular potentials in 2D. Mathematische Zeitschrift, 295, 3 (2020), 1521–1535. doi:10.1007/s00209-019-02436-0 arXiv:1704.06397
13. F. Zouari, M. Louati, S. Meniconi, E. Blåsten, M. S. Ghidaoui and B. Brunone, Experimental verification of the accuracy and robustness of Area Reconstruction Method for a Pressurized Water Pipe System. Journal of Hydraulic Engineering, ASCE, 146, 3 (2020). doi:10.1061/(ASCE)HY.1943-7900.0001674
14. E. Blåsten, F. Zouari, M. Louati and M. S. Ghidaoui, Blockage detection in networks: the area reconstruction method. Mathematics in Engineering, 1, 4 (2019). doi:10.3934/mine.2019.4.849 arXiv:1909.05497
15. F. Zouari, E. Blåsten, M. Louati, and M. S. Ghidaoui, Internal pipe area reconstruction as a tool for blockage detection. Journal of Hydraulic Engineering, ASCE, 145, 6 (2019) doi:10.1061/(ASCE)HY.1943-7900.0001602
16. E. Blåsten, Y.-H. Lin Radiating and non-radiating sources in elasticity. Inverse Problems, 35, 1 (2019), 015005. doi:10.1088/1361-6420/aae99e arXiv:1807.07225
17. E. Blåsten, Nonradiating sources and transmission eigenfunctions vanish at corners and edges. SIAM Journal on Mathematical Analysis, 50, 6 (2018), 6255–6270. doi:10.1137/18M1182048 arXiv:1803.10917
18. E. Blåsten, Well-posedness of the Goursat problem and stability for point source inverse backscattering, Inverse Problems, 33, 12 (2017), 125003. doi:10.1088/1361-6420/aa941f arXiv:1705.09442
19. E. Blåsten, H. Liu, On vanishing near corners of transmission eigenfunctions, Journal of Functional Analysis, 273, 11 (2017), 3616–3632. doi:10.1016/j.jfa.2017.08.023 arXiv:1701.07957
20. E. Blåsten, X. Li, H. Liu, Y. Wang, On vanishing and localizing of transmission eigenfunctions near singular points: A numerical study, Inverse Problems, 33, 10 (2017), 105001. doi:10.1088/1361-6420/aa8826 arXiv:1704.01885
21. E. Blåsten, J. Sylvester, Translation-Invariant Estimates for Operators with Simple Characteristics, Journal of Differential Equations, 263, 9 (2017), 5656–5695. doi:10.1016/j.jde.2017.06.033 arXiv:1607.06214
22. E. Blåsten, O. Yu. Imanuvilov, M. Yamamoto, Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials, Inverse Problems and Imaging, 9, 3 (2015), 709–723. doi:10.3934/ipi.2015.9.709 arXiv:1504.02207
23. E. Blåsten, L. Päivärinta, J. Sylvester, Corners Always Scatter, Communications in Mathematical Physics, 331, 2 (2014), 725–753. doi:10.1007/s00220-014-2030-0 arXiv:1211.1848
24. E. Blåsten, L. Päivärinta, Completeness of generalized transmission eigenstates, Inverse Problems, 29, 10 (2013), 104002. doi:10.1088/0266-5611/29/10/104002 arXiv:1307.4863

### Conference Proceedings

1. F. Zouari, M. Louati, E. Blåsten, and M. S. Ghidaoui, Multiple defects detection and characterization in pipes. 13th International Conference on Pressure Surges, Bordeaux, France, BHR Group, Nov. 2018, 217–231. ISBN:978-1-5108-7524-1

### Theses

1. E. Blåsten, On the Gel’Fand-Calderón inverse problem in two dimensions, Doctoral thesis, University of Helsinki, Faculty of Science, Department of Mathematics and Statistics, 2013. URN:ISBN:978-952-10-8699-1 arXiv:1307.4870
2. E. Blåsten, The Inverse Problem of the Schrödinger Equation in the Plane: A Dissection of Bukhgeim's Result, Licentiate thesis, University of Helsinki, Faculty of Science, Department of Mathematics and Statistics, 2010. arXiv:1103.6200
3. E. Blåsten, Distribuutioteorian alkeet ja sovellutuksia, Master’s thesis, University of Helsinki, Faculty of Science, Department of Mathematics and Statistics, 2008. PDF (in Finnish)

### Other publications

1. E. Blåsten, Y.-H. Lin, Corrigendum: Radiating and non-radiating sources in elasticity, Unpublished, (2021). PDF
2. E. Blåsten, H. Liu, Addendum to: "On vanishing near corners of transmission eigenfunctions", (2017), arXiv: 1710.08089. arXiv:1710.08089
3. E. Blåsten, Matematiikkaa Venäjällä, Solmu: matematiikkalehti, 3 (2007). https://matematiikkalehtisolmu.fi/2007/3/Dubna.pdf

## Talks

1. Inverse spectral problem on discrete graphs, Seminars on Inverse Problems, Theory and Applications; Organized by Dr. F. Ayça Çetinkaya (remote talk), 10 September 2024.
   Seminar Talk Videos
2. Determining the shape of a flat scattering screen with one measurement, Partial Differential Equations & Applied Mathematics Seminar; Drexel University, Philadelphia, USA, 7 June 2024.
   Event Talk
3. Scattering from corners and other singularities, Finnish Mathematical Days 2024; Aalto University, Espoo, Finland, 5 January 2024.
   Event Talk
4. Scattering from corners and other singularities, International Zoom Inverse Problems Seminar; UC Irvine (remote talk), 16 November 2023, at 9:00 am PST.
   Event Talk
5. Scattering from corners and other singularities and Imaging water supply pipes using pressure waves, Applied Inverse Problems Conference; University of Göttingen, Göttingen, Germany, 4 and 7 September 2023.
   Event Talk1 Talk2
6. Imaging water supply networks and vocal tracts, Inverse Days 2022; University of Eastern Finland, Tahko, Kuopio, Finland, 14 December 2022.
   Event Talk
7. Imaging water supply pipes using pressure waves, COPE—INAR workshop; LUT University, Lahti, Finland, 17 November 2022.
   Talk
8. Scattering from corvers and other singularities, Inverse problems in analysis and geometry; University of Helsinki, Helsinki, Finland, 4 August 2022.
   Event Talk
9. Inverse spectral problem on discrete graphs, SIAM 2022 Conference on Imaging Science; Berlin, Germany (remote talk), 25 March 2022.
   Event Session Talk
10. Inverse spectral problem on discrete graphs, Congreso Bienal de la Real Sociedad Matemática Española 2022; Ciudad Real, Spain (remote talk), 17 January 2022.
    Event Session Talk
11. Detecting blockages in water supply networks using boundary control, Inverse Days 2019; University of Jyväskylä, Finland, 17 December 2019.
    Event Talk
12. Inverse problems with one measurement, Inverse Days 2018; Aalto University, Finland, 12 December 2018.
    Event Talk
13. Inverse problems with one measurement, Inverse problems, PDE and geometry; University of Jyväskylä, Finland, 22 August 2018.
    Event Talk
14. Inverse problems with one measurement, The 9th International Conference on Inverse Problems and Related Topics; National University of Singapore, Singapore, 15 August 2018.
    Event-(link broken) Talk
15. Inverse backscattering with points–source waves, 3rd East Asia Section of IPIA, Young Scholars Symposion; Hong Kong Baptist University, Hong Kong, 17 March 2018.
    Event Talk
16. Applications of corner scattering: intrinsic properties of transmission eigenfunctions and single wave probing, Seminar; School of Mathematical Sciences, Fudan University, China, 5 December 2017.
    Event Talk
17. Planar inverse boundary value problem for Lp potentials with p>4/3, Analysis Seminar; Department of Mathematics and Statistics; University of Jyväskylä, Finland, 23 August 2017.
18. Inverse backscattering with point-source waves, Inverse Problems Seminar; Department of Mathematics and Statistics; University of Helsinki, Finland, 17 August 2017.
    Notes
19. Corners always scatter — quantitative results, Applied Inverse Problems Conference 2017; Zhejiang University, Hangzhou, China, 31 May 2017.
    Programme-(link broken) Event-(link broken) Talk
20. Transmission eigenfunction localization, Annual meeting of the Hong Kong Mathematical Society; The Hong Kong University of Science and Technology, Hong Kong, 20 May 2017.
    Talk
21. Topics in Corner Scattering: Non-Scattering Waves, Potential Probing with a Single Incident Wave, and the Interior Transmission Problem, NCTS PDE and Analysis Seminar; National Center for Theoretical Sciences, National Taiwan University, Taipei, Taiwan, 9 Marh 2017.
    Talk
22. Inverse scattering using a single incident wave, 2nd East Asia Section of IPIA, Young Scholars Symposium; National Center for Theoretical Sciences, National Taiwan University, Taipei, Taiwan, 5 November 2016.
    Programme Talk
23. Non-scattering energies, new resolvent estimates and other projects, 1st East Asia Symposium of IPIA; South University of Science and Technology, Shenzhen, China, 29 February 2016.
    Programme Talk
24. Non-scattering energies and interior transmission eigenvalues, Workshop on Inverse Problems and Related Topics; Zhejiang University, Hangzhou, China, 9 December 2015.
    Programme Talk
25. A new viewpoint to scattering theory à la Hörmander, Spectral and Analytic Inverse Problems, Thematic Programme on Inverse Problems; Institut Henri Poincaré, Paris, France, 4 May 2015.
    Programme Event Talk
26. Solving the Inverse Problem for the 2D Schrödinger Equation with Lp-potential, 17th Annual Workshop on Applications and generalizations of complex analysis; University of Aveiro, Aveiro, Portugal, 21 March 2015.
    Event-(link broken) Event calendar Talk
27. Solving the Inverse Problem for the 2D Schrödinger Equation with Lp-potential, The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications; Instituto de Ciencias Matemáticas (ICMAT) and the Universidad Autónoma de Madrid (UAM), Madrid, Spain, 9 July 2014.
    Event Talk
28. Completeness of the generalized transmission eigenstates, International Conference on Novel Directions in Inverse Scattering; University of Delaware, Delaware, USA, 29 July 2013.
    Event-(link broken) Grant Talk

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