The distribution of eigenvalues of partial differential operators

D. G. Vassiliev

Séminaire Équations aux dérivées partielles (Polytechnique) (1991-1992)

  • page 1-17

How to cite

top

Vassiliev, D. G.. "The distribution of eigenvalues of partial differential operators." Séminaire Équations aux dérivées partielles (Polytechnique) (1991-1992): 1-17. <http://eudml.org/doc/112034>.

@article{Vassiliev1991-1992,
author = {Vassiliev, D. G.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {spectral asymptotics; boundary value problems; elliptic operators},
language = {eng},
pages = {1-17},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {The distribution of eigenvalues of partial differential operators},
url = {http://eudml.org/doc/112034},
year = {1991-1992},
}

TY - JOUR
AU - Vassiliev, D. G.
TI - The distribution of eigenvalues of partial differential operators
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1991-1992
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 17
LA - eng
KW - spectral asymptotics; boundary value problems; elliptic operators
UR - http://eudml.org/doc/112034
ER -

References

top
  1. 1 D.G. Vasil'ev, Binomial asymptotics of the spectrum of a boundary value problem, Funktsional. Anal. i Prilozhen.17 (1983), no. 4, 79-81; English transl. in Functional Anal. Appl.17 (1984), 309-311. Zbl0583.35082MR725421
  2. 2 D.G. Vasil'ev, Two-term asymptotics of the spectrum of a boundary value problem under an interior reflection of general form, Funktsional. Anal. i Prilozhen.18 (1984), no. 1, 1-13; English transl. in Functional Anal. Appl.18 (1984), 267-277. Zbl0574.35032MR775930
  3. 3 D.G. Vasil'ev, Asymptotics of the spectrum of a boundary value problem, Trudy Moskov. Mat. Obshch.49 (1986), 167-237; English transl. in Trans. Moscow Math. Soc. (1987), 173-245. Zbl0632.58036MR853539
  4. 4 D.G. Vasil'ev and A.L. Gol'denveizer, Distribution of free vibration frequencies in two- and three-dimensional elastic bodies, Mekhanika i nauchno-tekhnicheskii progress, vol. 3, Mekhanika deformiruemogo tverdogo tela, Nauka, Moscow, 1988, pp. 223-236; English transl. in Mechanical Engineering and Applied Mechanics, vol. 3, Mechanics of Deformable Solids (N. Kh. Arutiunian, I. F. Obraztsov, and V. Z. Parton, eds.), Hemisphere Publ., New York, 1991, pp. 227-242. MR984140
  5. 5 D.G. Vasil'ev and Yu. G. Safarov, Branching Hamiltonian billiards, Dokl. Akad. Nauk SSSR301 (1988), no. 2, 271-275; English transl. in Soviet Math. Dokl.38 (1989), no. 1, 64-68. Zbl0671.58012MR967818
  6. 6 V. Ya. Ivriĭ, On the second term of the spectral asymptotics for the Laplace-Beltrami operator on manifolds with boundary, Funktsional. Anal. i Prilozhen.14 (1980), no. 2, 25-34; English transl. in Functional Anal. Appl.14 (1980), 98-106. Zbl0453.35068MR575202
  7. 7 I.P. Kornfel'd, Ya. G. Sinai, and S.V. Fomin, Ergodic theory, "Nauka", Moscow, 1980; English transl. (Cornfeld, Fomin, and Sinai), Springer-Verlag, Berlin and New York, 1982. Zbl0508.28008MR610981
  8. 8 B.M. Levitan, On the asymptotic behavior of the spectral function of a self-adjoint differential second order equation, Izv. Akad. Nauk SSSR Ser. Mat.16 (1952), no. 1, 325-352. (Russian) Zbl0048.32403MR58067
  9. 9 J.L. Lions and E. Magenes, Problemes aux limites non homogènes et applications, vol. 1, Dunod, Paris, 1968; English transl., Springer-Verlag, Berlin and New York, 1972. Zbl0165.10801MR247243
  10. 10 François Trèves, Introduction to pseudo-differential and Fourier integral operators, vols. 1, 2, Plenum Press, New York, 1980. Zbl0453.47027MR597145
  11. 11 M.A. Shubin, Pseudodifferential operators and spectral theory, "Nauka", Moscow, 1980; English transl., Springer-Verlag, Berlin and New York, 1986. Zbl0616.47040
  12. 12 J.J. Duistermaat and V.W. Guillemin, The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math.29 (1975), 39-79. Zbl0307.35071MR405514
  13. 13 Lars Hörmander, The spectral function of an elliptic operator, Acta Math.121 (1968), 193-218. Zbl0164.13201MR609014
  14. 14 Lars Hörmander, Fourier integral operators. I, Acta Math.127 (1971), 79-183. Zbl0212.46601MR388463
  15. 15 Victor Ivriĭ, Precise spectral asymptotics for elliptic operators acting in fiberings over manifolds with boundary, Lecture Notes in Math., vol. 1100, Springer-Verlag, Berlin and New York, 1984. Zbl0565.35002MR771297
  16. 16 R. Melrose, Weyl's conjecture for manifolds with concave boundary, Proc. Sympos. Pure Math., vol. 36, Amer. Math. Soc., Providence, R.I., 1980, pp. 257-273. Zbl0436.58024MR573438
  17. 17 R. Seeley, An estimate near the boundary for the spectral function of the Laplace operator, Amer. J. Math.102 (1980), 869-902. Zbl0447.35029MR590638
  18. 18 V.S. Buslaev, Scattered plane waves, spectral asymptotics and trace formulae in exterior problems, Dokl. Akad. Nauk. SSSR197 (1971), no. 5, 999-1002; English transl. in Soviet Math. Dokl.12 (1971), no. 2, 591-595. Zbl0224.47023MR278108
  19. 19 L. Schwartz, Théorie des distributions, Hermann, Paris, 1966. Zbl0962.46025MR209834
  20. 20 Lars Hörmander, The analysis of linear partial differential operators, vol. 1, Springer-Verlag, Berlin and New York, 1983. Zbl0521.35001

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.