Geodesic
Extremal properties of discrete measures, the universal sequence, and the duality principle
Sbornik. Mathematics, Tome 189 (1998) no. 11, pp. 1587-1610 
M. L. Gerver; E. A. Kudryavtseva. Extremal properties of discrete measures, the universal sequence, and the duality principle. Sbornik. Mathematics, Tome 189 (1998) no. 11, pp. 1587-1610. http://geodesic.mathdoc.fr/item/SM_1998_189_11_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A new proof of results on the universal sequence and extremal properties of discrete measures is given on the basis of the duality principle. These results were earlier obtained by the same authors in the solution of certain maximum problems arising in mathematical geophysics. The transition to the dual minimum problems reveals the geometric meaning of these results and opens the way to their generalization.

[1] Gerver M. L., Kudryavtseva E. A., “Novoe dokazatelstvo teorem ob universalnoi posledovatelnosti i ekstremalnykh svoistvakh diskretnykh mer”, UMN, 52:6 (1997), 153–154 | MR | Zbl

[2] Gerver M. L., Novoe v klassicheskoi zadache obrascheniya godografa, Preprint, MITP RAN, 1997 ; Вопросы геодинамики и сейсмологии. Вычислительная сейсмология, No 30, Наука, М., 1998 | MR

[3] Gerver M. L., Kudryavtseva E. A., “Ob ekstremalnykh svoistvakh volnovodov s konechnym chislom sloev v zadache obrascheniya godografa”, Dokl. AN, 356:1 (1997), 25–28 | MR | Zbl

[4] Gerver M. L., Kudryavtseva E. A., “Universalnaya posledovatelnost v klassicheskoi zadache obrascheniya godografa”, Matem. sb., 188:4 (1997), 3–56 | MR | Zbl

[5] Kronrod A. S., Uzly i vesa kvadraturnykh formul, Nauka, M., 1964

[6] Krein M. G., Nudelman A. A., Problema momentov Markova i ekstremalnye zadachi, Nauka, M., 1973 | MR

[7] Karlin S., Stadden V., Chebyshevskie sistemy i ikh primenenie v analize i statistike, Nauka, M., 1976 | MR

[8] Gantmakher F. R., Krein M. G., Ostsillyatsionnye matritsy i yadra i malye kolebaniya mekhanicheskikh sistem, GITTL, M.–L., 1950

[9] Gerver M. L., Kudryavtseva E. A., “Teorema ob otnosheniyakh predshestvovaniya, generiruemykh vpolne polozhitelnymi yadrami”, Matem. sb., 186:9 (1995), 19–44 | MR | Zbl

[10] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1972