|
|
|
|
Список литературы
|
|
| |
| 1. |
Арнольд В. И., Лекции об уравнениях с частными производными, ФАЗИС, М., 1997  |
| 2. |
Арнольд В. И. и др., “Некоторые нерешенные задачи теории дифференциальных уравнений и
математической физики”, Успехи мат. наук, 44:4(268) (1989), 191–202  |
| 3. |
Erdélyi A., Magnus W., Oberhettinger F., Tricomi F. G., Higher transcendental functions, vol. II, McGraw-Hill Book Co., Inc., New York etc., 1953 |
| 4. |
Bérard P., Volume des ensembles nodaux des fonctions propres du laplacien, Bony–Sjöstrand–Meyer Seminar (1984–1985), Exp. No. 14, École Polytech., Palaiseau, 1985 |
| 5. |
Brüning J., “Über Knoten von Eigenfunktionen des Laplace–Beltrami Operators”, Math. Z., 158 (1978), 15–21   |
| 6. |
Cheng S.-Y., “Eigenfunctions and nodal sets”, Comment. Math. Helv., 51 (1976), 43–55 |
| 7. |
Courant R., Hilbert D., Methoden der mathematischen Physik, Bd. 1, Grundlehren Math. Wiss., 12, Springer-Verlag, Berlin, 1931 |
| 8. |
Donnelly H., Fefferman C., “Nodal sets of eigenfunctions on Riemannian manifolds”, Invent. Math., 93:1 (1988), 161–183  |
| 9. |
Eremenko A., Jakobson D., Nadirashvili N., On nodal sets and nodal domains on $\mathbb S^2$ and $\mathbb R^2$, Preprint arXiv:math.SP/0611627 |
| 10. |
Federer H., Geometric measure theory, Grundlehren Math. Wiss., 153, Springer, Berlin, 1969 |
| 11. |
Gichev V. M., “A note on common zeroes of Laplace–Beltrami eigenfunctions”, Ann. Global Anal. Geom., 26 (2004), 201–208 |
| 12. |
Lewy H., “On the minimum number of domains in which the nodal
lines of spherical harmonics divide the sphere”, Comm. Partial Differential Equations, 2:12 (1977), 1233–1244 |
| 13. |
Mangoubi D., On the inner radius of nodal domains, arXiv:math/0511329v3 |
| 14. |
Mangoubi D., Local asymmetry and the inner radius of nodal domains, arXiv:math/0703663v3 |
| 15. |
Maxwell J. C., A treatise on electricity and magnetism, vol. 1, Dover Publ., Inc., New York, 1954 |
| 16. |
Neuheisel J., The asymptotic distribution of nodal sets on spheres, Johns Hopkins Ph. D. thesis, 2000 |
| 17. |
Rudnick Z., Wigman I., On the volume of nodal sets for eigenfunctions of the Laplacian on the torus, Preprint arXiv:math-ph/0609072v2 |
| 18. |
Savo A., “Lower bounds for the nodal length of eigenfunctions of the Laplacian”, Ann. Global Anal. Geom., 19 (2001), 133–151 |
| 19. |
Stein E., Weiss G., Introduction to Fourier analysis on Euclidean spaces, Princeton Math. Ser., 32, Princeton Univ. Press, Princeton, NJ, 1971 |
| 20. |
Sylvester J. J., “Note on spherical harmonics”, Philos. Mag., 2 (1876), 291–307 |
| 21. |
Szegö G., Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., 23, Amer. Math. Soc., Providence, RI, 1959 |
| 22. |
Yau S. T. (ed.), Seminar on Differential Geometry, Ann. of Math. Stud., 102, Princeton Univ. Press, Princeton, NJ, 1982 |
