Voir la notice de l'article provenant de la source Math-Net.Ru
@article{IVM_2000_10_a2,
author = {B. A. Kats},
title = {The {Stieltjes} integral along a~fractal contour and some of its applications},
journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
pages = {21--32},
publisher = {mathdoc},
number = {10},
year = {2000},
language = {ru},
url = {https://geodesic-test.mathdoc.fr/item/IVM_2000_10_a2/}
}
B. A. Kats. The Stieltjes integral along a~fractal contour and some of its applications. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2000), pp. 21-32. https://geodesic-test.mathdoc.fr/item/IVM_2000_10_a2/
[1] Mandelbrot B., The fractal geometry of nature, Freeman, San Francisco, 1982 | MR | Zbl
[2] Feder E., Fraktaly, Mir, M., 1991, 280 pp. | MR
[3] Kats B. A., “Zadacha o skachke i integral po nespryamlyaemoi krivoi”, Izv. vuzov. Matematika, 1987, no. 5, 49–57 | MR | Zbl
[4] Harrison J., Norton A., “Geometric integration on fractal curves in the plane”, Indiana Math. J., 40:2 (1991), 567–594 | DOI | MR | Zbl
[5] Kats B. A., “O kraevoi zadache Rimana na fraktalnoi duge”, Dokl. RAN, 333:4 (1993), 432–433 | MR | Zbl
[6] Kats B. A., “Ob odnoi versii kraevoi zadachi Rimana na fraktalnoi krivoi”, Izv. vuzov. Matematika, 1994, no. 4, 10–20 | MR | Zbl
[7] Harrison J., Norton A., “The Gauss–Green theorem for fractal boundaries”, Duke Math. J., 67:3 (1992), 575–586 | DOI | MR
[8] Harrison J., “Stokes' theorem for nonsmooth chains”, Bull. of Amer. Math. Soc., 29:2 (1993), 235–242 | DOI | MR | Zbl
[9] Ob'edkov T. E., “Primenenie nestandartnogo analiza k teorii integrirovaniya i reshenie zadachi Rimana o skachke”, Algebra i analiz, Tez. dokl. mezhd. konf., posv. 100-letiyu N. G. Chebotareva. Ch. II, Kazan, 1994, 96–97
[10] Kats B. A., “Ob integrirovanii po nespryamlyaemoi krivoi”, Vopr. matem., mekhan. sploshn. sred i primeneniya matem. metodov v stroitelstve, MISI, Moskva, 1992, 63–69
[11] Kats B. A., “Integrirovanie po ploskoi fraktalnoi krivoi, zadacha o skachke i obobschennye mery”, Izv. vuzov. Matematika, 1998, no. 10, 53–65 | MR | Zbl
[12] Kats B. A., “Integrirovanie po fraktalnoi krivoi i zadacha o skachke”, Matem. zametki, 64:4 (1998), 549–557 | MR | Zbl
[13] Kondurar V., “Ob integrale Stiltesa”, Matem. sb., 2:2 (1937), 361–366
[14] Wiener N., “The quadratic variation of a function and its Fourier coefficients”, Massachusetts J. of Math., 3 (1924), 72–94 | Zbl
[15] Young L. C., “An inequality of the Holder type, connected with Stieltjes integration”, Acta Math., Uppsala, 36:3–4 (1936), 251–282 | DOI | MR
[16] Young L. C., “General inequalities for Stieltjes integrals and the convergence of Fourier series”, Math. Annalen, Berlin, 115:4 (1938), 581–612 | DOI | MR
[17] Dyachkov A. M., “O suschestvovanii integrala Stiltesa”, Dokl. RAN, 350:2 (1996), 158–161 | MR
[18] Burkill J. C., “Differential properties of Young–Stieltjes integrals”, J. London Math. Soc., 23 (1):89 (1948), 22–28 | DOI | MR | Zbl
[19] Khërmander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi. T. 1. Teoriya raspredelenii i analiz Fure, Mir, M., 1986, 462 pp.
[20] Kats B. A., “Zadacha Rimana na zamknutoi zhordanovoi krivoi”, Izv. vuzov. Matematika, 1983, no. 4, 68–80 | MR | Zbl
[21] Muskhelishvili N. I., Singulyarnye integralnye uravneniya. Granichnye zadachi teorii funktsii i nekotorye ikh prilozheniya k matematicheskoi fizike, Fizmatgiz, M., 1962, 599 pp.
[22] Gakhov F. D., Kraevye zadachi, Nauka, M., 1977, 640 pp. | MR
[23] Vekua I. N., Obobschennye analiticheskie funktsii, Nauka, M., 1988, 509 pp. | MR | Zbl
[24] Dynkin E. M., “Gladkost integralov tipa Koshi”, Zap. nauchn. semin. LOMI AN SSSR, 92, 1979, 115–133 | MR