An extension of Krein's inverse spectral theorem to strings with nonreflecting left boundaries

Uwe Küchler; Kirsten Neumann

Séminaire de probabilités de Strasbourg (1991)

  • Volume: 25, page 354-373

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Küchler, Uwe, and Neumann, Kirsten. "An extension of Krein's inverse spectral theorem to strings with nonreflecting left boundaries." Séminaire de probabilités de Strasbourg 25 (1991): 354-373. <http://eudml.org/doc/113772>.

@article{Küchler1991,
author = {Küchler, Uwe, Neumann, Kirsten},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {gap diffusion; elastic boundary; generalized differential operator; spectral theorem; killing boundary},
language = {eng},
pages = {354-373},
publisher = {Springer - Lecture Notes in Mathematics},
title = {An extension of Krein's inverse spectral theorem to strings with nonreflecting left boundaries},
url = {http://eudml.org/doc/113772},
volume = {25},
year = {1991},
}

TY - JOUR
AU - Küchler, Uwe
AU - Neumann, Kirsten
TI - An extension of Krein's inverse spectral theorem to strings with nonreflecting left boundaries
JO - Séminaire de probabilités de Strasbourg
PY - 1991
PB - Springer - Lecture Notes in Mathematics
VL - 25
SP - 354
EP - 373
LA - eng
KW - gap diffusion; elastic boundary; generalized differential operator; spectral theorem; killing boundary
UR - http://eudml.org/doc/113772
ER -

References

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  1. [1] Dym, H.; McKean, H.P., Gaussian processes, function-theory and the inverse spectral theorem, New York, Academic Press (1976). Zbl0327.60029
  2. [2] Ito, K.; McKean, H.P., Diffusion Processes and their Sample Paths, 2nd Printing, Springer, Berlin (1974). Zbl0285.60063MR345224
  3. [3] Kac, I.S.; Krein, M.G., On the spectral functions of the string, Amer. Math. Soc. Transl., (2) 103 (1974), 19-102. Zbl0291.34017
  4. [4] Karlin, S.; McGregor, J., The differential equations of the birth- and death processes and the Stieltjes moment problem, Trans. Amer. Math. Soc.85(1957), 489-546. Zbl0091.13801MR91566
  5. [5] Knight, F.B., Characterization of the Lévy measures of inverse local times of gap diffusion, Progress in Prob. Statist.1, Birkhäuser, Boston, Mass.1981. Zbl0518.60083MR647781
  6. [6] Kotani, S.; Watanabe, S., Krein's spectral theory of strings and generalized diffusion processes, Lecture Notes of Mathematics Vol. 923, (1981), 235-259. Zbl0496.60080MR661628
  7. [7] Küchler, U., Some Asymptotic Properties of the Transition Densities of One-Dimensional Quasidiffusion, Publ. RIMS, Kyoto-University, 16(1980), 245-268. Zbl0443.60077MR574035
  8. [8] Küchler, U., On sojourn times, excursions and spectral measures connected with quasidiffusions, J. Math. Kyoto University, 26(1986), 403-421. Zbl0625.60093MR857226
  9. [9] Küchler, U.; Salminen, P., On spectral measures of strings and excursions of quasidiffusions, Lecture Notes of Mathematics Vol. 1372, (1989), 490-502. Zbl0731.60071MR1022933
  10. [10] Neumann, K., Asymptotische Eigenschaften von Quasidiffusionen und eine Verallgemeinerung des Kreinschen Spektralsatzes, Dissertation A, Humboldt-UniversitätBerlin, 1989. 

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