Geodesic
On asymptotic decay of the eigenfunctions of elliptic operators
Eurasian mathematical journal, Tome 1 (2010) no. 2, pp. 99-109.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is known that eigenfunctions of many elliptic operators such as Schrödinger operators decrease exponentially. It this paper we suggest a different idea of the proof of this fact. This idea is based on a special transformation $\Psi_\varepsilon$. 
@article{EMJ_2010_1_2_a6,
     author = {V. G. Kurbatov},
     title = {On asymptotic decay of the eigenfunctions of elliptic operators},
     journal = {Eurasian mathematical journal},
     pages = {99--109},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2010_1_2_a6/}
}
TY  - JOUR
AU  - V. G. Kurbatov
TI  - On asymptotic decay of the eigenfunctions of elliptic operators
JO  - Eurasian mathematical journal
PY  - 2010
SP  - 99
EP  - 109
VL  - 1
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2010_1_2_a6/
LA  - en
ID  - EMJ_2010_1_2_a6
ER  - 
%0 Journal Article
%A V. G. Kurbatov
%T On asymptotic decay of the eigenfunctions of elliptic operators
%J Eurasian mathematical journal
%D 2010
%P 99-109
%V 1
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2010_1_2_a6/
%G en
%F EMJ_2010_1_2_a6
V. G. Kurbatov. On asymptotic decay of the eigenfunctions of elliptic operators. Eurasian mathematical journal, Tome 1 (2010) no. 2, pp. 99-109. http://geodesic.mathdoc.fr/item/EMJ_2010_1_2_a6/

[1] S. Agmon, Lectures on exponential decay of solutions of second-order elliptic equations: bounds on eigenfunctions of $N$-body Schrödinger operators, Mathematical Notes, 29, Princeton University Press, Princeton, N.J., 1982 | MR | Zbl

[2] C. Bardos, M. Merigot, “Asymptotic decay of the solutions of a second order elliptic equation in an unbounded domain. Applications to the spectral propreties of a Hamiltonian”, Proc. Royal Soc. Edinburg A, 76 (1977), 323–344 | MR | Zbl

[3] V. I. Burenkov, Sobolev Spaces on Domains, B. G. Teubner, Stuttgart, Leipzig, 1998 | MR | Zbl

[4] J. J. F. Founier, J. Stewart, “Amalgams of $L^p$ and $l^q$”, Bull. Amer. Math. Soc., 13 (1985), 1–21 | DOI | MR

[5] R. Froese, I. Herbst, M. Hoffmann-Ostenhof, Th. Hoffmann-Ostenhof, “$L^2$-exponential lower bounds to solutions of the Schrödinger equation”, Commun. Math. Phys., 87 (1982), 265–286 | DOI | MR | Zbl

[6] Functional Analysis, ed. S. G. Krein, Wolters-Noordhooff Publishing, Groningen, 1972 | MR

[7] T. Kato, Perturbation Theory of Linear Operators, Springer Verlag, Berlin, Heidelberg, New York, 1966 | MR

[8] V. G. Kurbatov, Functional Differential Operators and Equations, Kluwer Academic, Dordrecht, Boston, London, 1999 | MR | Zbl

[9] J.-L. Lions, E. Magenes, Problèmes aux Limites non Homogènes et applications, v. 1, Dunod, Paris, 1968

[10] M. Reed, B. Simon, Methods of Modern Mathematical Physics, v. I, Functional Analysis, Academic Press, New York, London, 1972

[11] W. Rudin, Functional Analysis, McGraw-Hill Book Company, New York, 1990 | MR

[12] L. Schwartz, Théorie des Distributions, v. I, II, Hermann, Paris, 1966 | MR

[13] Translations of Mathematical Monographs, 90, AMS, 1991 | MR | MR | Zbl

[14] M. E. Taylor, Pseudodifferential Operators, Prinseton Univ. Press, Prinseton, New Jersey, 1981 | MR | Zbl

[15] M. E. Taylor, Partial Differential Equations, v. I, Basic Theory, Springer, New York, Berlin, 1996 | MR