The periodic analog of Rolle's theorem for differential operators and approximation by $L$-splines
Matematičeskie zametki, Tome 56 (1994) no. 4, pp. 102-113.

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S. I. Novikov. The periodic analog of Rolle's theorem for differential operators and approximation by $L$-splines. Matematičeskie zametki, Tome 56 (1994) no. 4, pp. 102-113. http://geodesic.mathdoc.fr/item/MZM_1994_56_4_a9/

[1] Babenko V. F., Ligun A. A., “Ekstremalnye svoistva polinomov i splainov”, Modelirovanie v mekhanike, 5(22):5 (1991), 5–13 | MR | Zbl

[2] Krein M. G., “K teorii nailuchshego priblizheniya periodicheskikh funktsii”, DAN SSSR, 18:4–5 (1938), 245–249 | Zbl

[3] Nguen Tkhi Tkheu Khoa, Nailuchshie kvadraturnye formuly i metody vosstanovleniya na klassakh funktsii, zadavaemykh svertkami, ne uvelichivayuschimi ostsillyatsiyu, Dis. ...kand. fiz.-matem. nauk, MGU, M., 1985

[4] Novikov S. I., Priblizhenie funktsii $L$-splainami, Dis. ...kand. fiz.-mat. nauk, In-t matematiki i mekhaniki UNTs AN SSSR, Sverdlovsk, 1986

[5] Shevaldin V. T., Ekstremalnaya interpolyatsiya dlya lineinykh differentsialnykh operatorov s postoyannymi koeffitsientami, Dis. ...kand. fiz.-mat. nauk, UrGU, Sverdlovsk, 1983

[6] Morsche H. G., Interpolation and extremal properties of $L$-spline functions, Proefschrift graad doct. techn. wetenschappen tech. Hogesch, Eindhoven, 1982

[7] Sun Yongsheng, Huang Da-ren, “On $N$-widths of generalized Bernoulli kernel”, Approx. Theory Appl., 1:2 (1985), 83–92 | MR | Zbl

[8] Levin A. Yu., “Neostsillyatsiya reshenii uravneniya $x^n+p_1(t)x^{(n-1)} +\dots +p_n(t) x=0$”, UMN, 24:2 (1969), 42–96

[9] Coppel W. A., “Disconjugacy”, Lecture Notes in Math., 220, 1971, 1–148 | MR

[10] Troch I., “On the interval of disconjugacy of linear autonomous differential equations”, SIAM J. Math. Analysis, 12:1 (1981), 78–89 | DOI | MR | Zbl

[11] Etgen G., Jones G., Taylor W. E., “On the factorization of ordinary linear differential operators”, Trans. Amer. Math. Soc., 297:2 (1986), 717–728 | DOI | MR | Zbl

[12] Zettl A., “General theory of the factorization of ordinary linear differential operators”, Trans. Amer. Math. Soc., 197:1 (1974), 341–353 | DOI | MR | Zbl

[13] Levin A. Yu., “Faktorizatsiya Poia–Mammana v periodicheskom sluchae”, Vestn. Yaroslavskogo un-ta, no. 2, 1973, 57–59 | MR

[14] Krein M. G., “Ob odnom novom svoistve operatora Shturma–Liuvillya”, Trudy Odeskogo un-ta, Sb. matem. otdel. fiz.-matem. fak., Odesskii un-t, Odessa, 1941, 15–22

[15] Nguen Tkhi Tkheu Khoa, “Ostsillyatsionnye svoistva differentsialnykh operatorov i operatorov svertki i nekotorye prilozheniya”, Izv. AN SSSR. Ser. matem., 53:3 (1989), 590–606

[16] Nguen Tkhi Tkheu Khoa, “Operator $D(D^2+1^2)\dots (D^2+n^2)$ i trigonometricheskaya interpolyatsiya”, Analysis Math., 15:4 (1989), 291–306 | MR

[17] Trikomi F., Differentsialnye uravneniya, Izd-vo IL, M., 1962

[18] Melentsova Yu. A., Milshtein G. N., “K optimalnoi otsenke promezhutka neostsillyatsii dlya lineinykh differentsialnykh uravnenii s ogranichennymi koeffitsientami”, Differents. uravneniya, 17:12 (1981), 2160–2175 | MR | Zbl

[19] Milshtein G. N., “O kraevoi zadache dlya sistemy dvukh differentsialnykh uravnenii”, Differents. uravneniya, 1:12 (1965), 1628–1639 | MR

[20] Novikov S. I., “O suschestvovanii sovershennykh $L$-splainov s zadannymi nulyami, opredelyaemykh lineinymi differentsialnymi operatorami s peremennymi periodicheskimi koeffitsientami”, Ryady Fure: teoriya i prilozheniya, AN Ukrainy In-t matematiki, Kiev, 1992, 64–68

[21] Korneichuk N. P., Tochnye konstanty v teorii priblizheniya, Nauka, M., 1987

[22] Shevaldin V. T., “Interpolyatsionnye periodicheskie $L$-splainy s ravnomernymi uzlami”, Priblizhenie funktsii polinomami i splainami, AN SSSR UNTs In-t matematiki i mekhaniki, Sverdlovsk, 1985, 140–147 | MR

[23] Tikhomirov V. M., “Nailuchshie metody priblizheniya i interpolirovaniya differentsiruemykh funktsii v $C_{[-1;1]}$”, Matem. sb., 80:2 (1969), 290–304 | MR | Zbl