Ir al contenido

Documat


De Branges functions of Schroedinger equations

  • Autores: Alexander Baranov, Yurii Belov, Alexei Poltoratski
  • Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 68, Fasc. 2, 2017, págs. 251-263
  • Idioma: inglés
  • DOI: 10.1007/s13348-016-0168-0
  • Texto completo no disponible (Saber más ...)
  • Resumen
    • We characterize the Hermite–Biehler (de Branges) functions E which correspond to Schroedinger operators with L^2 potential on the finite interval. From this characterization one can easily deduce a recent theorem by Horvath. We also obtain a result about location of resonances.

  • Referencias bibliográficas
    • Abakumov, E., Baranov, A., Belov, Y.: Localization of zeros for Cauchy transforms. Int. Math. Res. Not. 2015, 6699–6733 (2015)
    • Chelkak, D.: An application of the fixed point theorem to the inverse Sturm–Liouville problem. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat....
    • de Branges, L.: Hilbert Spaces of Entire Functions. Prentice-Hall, Englewood Cliffs (1968)
    • Dym, H., McKean, H.P.: Gaussian Processes, Function Theory and the Inverse Spectral Problem. Academic Press, New York (1976)
    • Hitrik, M.: Bounds on scattering poles in one dimension. Commun. Math. Phys. 208(2), 381–411 (1999)
    • Horváth, M.: Inverse spectral problems and closed exponential systems. Ann. Math. 162(2), 885–918 (2005)
    • Iantchenko, A., Korotyaev, E.: Resonances for Dirac operators on the half-line. J. Math. Anal. Appl. 420(1), 279–313 (2014)
    • Korotyaev, E.: Inverse resonance scattering on the half line. Asymptot. Anal. 37(3–4), 215–226 (2004)
    • Lagarias, J.: Zero spacing distributions for differenced L-functions. Acta Arith. 120(2), 159–184 (2005)
    • Lagarias, J.: The Schrödinger operator with Morse potential on the right half line. Commun. Number Theory Phys. 3(2), 323–361 (2009)
    • Levin, B.Ya.: Distribution, of Zeros of Entire Functions. Am. Math. Soc., Providence (1964). [Revised edition: Am. Math. Soc., Providence...
    • Marchenko, V.A.: Certain problems in the theory of second-order differential operators. Dokl. Akad. Nauk SSSR 72, 457–460 (1950). (Russian)
    • Marchenko, V.A.: Some questions in the theory of one-dimensional linear differential operators of the second order. I, Trudy Moskov. Mat....
    • Makarov, N., Poltoratski, A.: Meromorphic inner functions, Toeplitz kernels, and the uncertainty principle. In: Perspectives in Analysis,...
    • Poshel, J., Trubowitz, E.: Inverse Spectral Theory. Academic Press, New York (1987)
    • Remling, C.: Schrödinger operators and de Branges spaces. J. Funct. Anal. 196, 323–394 (2002)
    • Romanov, R.: Canonical systems and de Branges spaces. arXiv:1408.6022
    • Romanov, R.: Order problem for canonical systems and a conjecture of Valent. Trans. Am. Math. Soc. arXiv:1502.04402
    • Simon, B.: Resonances in one dimension and Fredholm determinants. J. Funct. Anal. 178(2), 396–420 (2000)

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno