Extremal spectral quantities and related problems

Publications within the scope of this project:


    45. J.B. Kennedy
          A family of diameter-based eigenvalue bounds for quantum graphs

          Discrete and Continuous Models in the Theory of Networks, Operator Theory: Advances and Applications,
          Birkhäuser 2019, F. Atay, P. Kurasov and D. Mugnolo (eds),

    44. P. Freitas and R.S. Laugesen
          From Steklov to Neumann and beyond, via Robin: the Szegö way
          Canadian J. Math.

    43. D. Krejčiřík, V. Lotoreichik and T. Ourmieres-Bonafos
          Spectral transitions for Aharonov-Bohm Laplacians on conical layers

          Proc. Roy. Soc. Edinburgh Sect. A.

 Published Articles

    42. G. Berkolaiko, J.B. Kennedy P. Kurasov and D. Mugnolo,
          Surgery principles for the spectral analysis of quantum graphs

          Trans. Amer. Math. Soc. 372 (2019), 5153--5197

    41. P.R.S. Antunes, D. Buoso and P. Freitas
          On the behaviour of clamped plates under large compression

          SIAM J. Appl. Math. 79 (2019), 1872-1891.

    40. F. Della Pietra, N. Gavitone and G. Piscitelli
          On the second Dirichlet eigenvalue of some nonlinear anisotropic elliptic operators

          Bull. Sci. Math. 155 (2019), 10-32.

    39. N. C. Dias and J. Prata
          A refinement of the Robertson-Schrödinger uncertainty principle and a Hirschman-Shannon inequality for Wigner distributions

          J. Fourier Anal. Appl. 25 (2019), 210-241.

    38. C.J.S.Alves and P.R.S. Antunes
          Determination of elastic resonance frequencies and eigenmodes using the method of fundamental solutions

          Engineering Analysis with Boundary Elements 101 (2019), 330-342.

    37. N. C. Dias and J. Prata
          Quantum mappings acting by coordinate transformations on Wigner distributions

          Rev. Mat. Iberoamericana 35 (2019), 317–337.

    36. P. Freitas
          A remark on Pólya's conjecture at low frequencies
          Arch. Math. (Basel) 112 (2019), 305-311.

    35. J.S. Ben-Benjamin, N. C. Dias, L. Cohen, P. Loughlin, and J. Prata
          What is the Wigner function closest to a given square integrable function?

          SIAM J. Math. Anal. 50 (2018), 5161–5197.

    34. C. Aldana and J. Rowlett
          A Polyakov formula for sectors

          J. Geom. Anal. 28 (2018), 1773–1839.

    33. B. Kawohl and D. Krejčiřík
          From Symmetry to Monotonicity

          Math. Intell. 40 (2018), 12-13.

    32. D. Krejčiřík and R. Tiedra de Aldecoa
          Ruled strips with asymptotically diverging twisting

          Ann. Henri Poincaré 19 (2018), 2069-2086.

    31. P.R.S. Antunes and F. Gazzola
          Some solutions of minimaxmax problems for the torsional displacements of rectangular plates

          Z Angew Math Mech. 98 (2018), 1974-1991.

    30. P.R.S. Antunes
          A numerical algorithm to reduce the ill conditioning in meshless methods for the Helmholtz equation

          Numer. Algorithms 79 (2018), 879-897

    29. P. Freitas
          The spectral determinant of the isotropic quantum harmonic oscillator in arbitrary dimensions
          Math. Ann. 372 (2018), 1081–1101

    28. N. C. Dias and J. Prata
          Wigner functions on non-standard symplectic vector spaces

          J. Math. Phys. 59 (2018), 012108.

    27. W. Kirsch, D. Krejčiřík and G. Raikov
          Lifshits tails for randomly twisted quantum waveguides

          J. Stat. Phys. 171 (2018), 383-399.

    26. D. Krejčiřík, N. Raymond, J. Royer and P. Siegl
          Reduction of dimension as a consequence of norm-resolvent convergence and applications

          Mathematika 64 (2018), 406-429.

    25. C.J.S. Alves and P.R.S. Antunes,
          The Method of Fundamental Solutions applied to boundary value problems on the surface of a sphere

          Comput. Math. Appl. 75 (2018), 2365-2373.

    24. P.R.S. Antunes
          Reducing the ill conditioning in the Method of Fundamental Solutions

          Adv. Comput. Math. 44 (2018), 351-365.

    23. P.R.S. Antunes, S. A. Mohammadi and H. Voss
          A nonlinear eigenvalue optimization problem: optimal potential functions

          Nonlinear Analysis Series B: Real World Applications 46 (2018), 307-327.

    22. P. Freitas, P. Siegl and C. Tretter
          The damped wave equation with unbounded damping
          J. Differential Eq. 264 (2018), 7023-7054.

    21. D. Krejčiřík and V. Lotoreichik
          Optimisation of the lowest Robin eigenvalue in the exterior of a compact set

          J. Convex Anal. 25 (2018), 319-337.

    20. J.B. Kennedy
          A toy Neumann analogue of the nodal line conjecture

          Arch. Math. (Basel) 110 (2018), 261-271.

    19. J.P. Dias and P. Freitas
          Decay of solutions for a class of nonlinear Schrödinger equations in R and the stability of shock profiles for a quasilinear Benney system
          Nonlinearity 31 (2018), 1110-1119.

    18. P. Freitas
          Sharp bounds for the modulus and phase of Hankel functions with applications to Jaeger integrals
          Math. Comp. 87 (2018), 289-308.

    17. O. Rouby
          Berezin-Toeplitz quantization and complex Weyl quantization of the torus T2.

          Portugaliae. Math. 74 (2017), 315-354.

    16. P.R.S. Antunes
          Harmonic configurations of non-homogeneous membranes

          Acta Acust united Ac 103 (2017), 596-606

    14. D. Borisov and P. Freitas
          The spectrum of geodesic balls on spherically symmetric manifolds

          Comm. Anal. Geom. 25 (2017), 507-544.

    13. G. Berkolaiko, J.B. Kennedy P. Kurasov and D. Mugnolo,
          Edge connectivity and the spectral gap of combinatorial and quantum graphs

          J. Phys. A: Math. Theor. 50 (2017), 365201 (29pp)

    12. P. Freitas and J. Lipovský
          Eigenvalue asymptotics for the damped wave equation on metric graphs

          J. DIfferential Eq. 263 (2017), 2780-2811.

    11. P.R.S. Antunes and E. Oudet
          Numerical minimization of Dirichlet-Laplacian eigenvalues of four-dimensional geometries

          SIAM J. Sci. Computing 39 (2017), 8508-8521.

    10. P.R.S. Antunes and E. Oudet
          Numerical results for extremal problem for eigenvalues of the Laplacian

          in Shape optimization and spectral theory, 2017, 398-411, Antoine Henrot (ed.), De Gruyter.

      9. D. Bucur, P. Freitas and J.B. Kennedy
          The Robin problem

          in Shape optimization and spectral theory, 2017, 78-119, Antoine Henrot (ed.), De Gruyter.

      8. P. Freitas and D. Krejčiřík
          A lower bound to the spectral threshold in curved quantum layers

          Functional Analysis and Operator Theory for Quantum Physics (2017), 261-269
          volume dedicated to Pavel Exner on the occasion of his 70th birthday
          J. Dittrich, H. Kovarik, and A. Laptev (eds.), EMS Publishing House.

      7. P.R.S. Antunes
          Is it possible to tune a drum?

          J. Comput. Physics 338 (2017), 91-106.

      6. P.R.S. Antunes, C. Barbarosie and A.M. Toader,
          Detection of holes in an elastic body based on eigenvalues and traces of eigenmode

          J. Comput. Physics 333 (2017), 352-368.

      5. P. Freitas
          Asymptotic behaviour of extremal averages of Laplacian eigenvalues
          J. Stat. Phys. 167 (2017), 1511-1518.

      4. P.R.S. Antunes and R.A.C. Ferreira
          Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives

          Commun. Nonlinear Sci. Numer. Simulat. 48 (2017), 398-413.

      3. N. C. Dias, C. Jorge and J. Prata
          One-dimensional Schrödinger operators with singular potentials: A Schwartz distributional formulation

          J. Differential Eq. 260 (2016), 6548-6580.

      2. P.R.S. Antunes
          Maximal and minimal norm of Laplacian eigenfunctions in a given subdomain

          Inverse Prob. 32 (2016), 115003.

      1. P. Freitas and J.B. Kennedy
          Summation formula inequalities for eigenvalues of Schrödinger operators

          J. Spectral Theory 6 (2016), 483-503.