Geodesic
Integration over a~plane fractal curve, a~jump problem and generalized measures
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (1998), pp. 53-65.

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

@article{IVM_1998_10_a7,
     author = {B. A. Kats},
     title = {Integration over a~plane fractal curve, a~jump problem and generalized measures},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {53--65},
     publisher = {mathdoc},
     number = {10},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_1998_10_a7/}
}
TY  - JOUR
AU  - B. A. Kats
TI  - Integration over a~plane fractal curve, a~jump problem and generalized measures
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 1998
SP  - 53
EP  - 65
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_1998_10_a7/
LA  - ru
ID  - IVM_1998_10_a7
ER  - 
%0 Journal Article
%A B. A. Kats
%T Integration over a~plane fractal curve, a~jump problem and generalized measures
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 1998
%P 53-65
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_1998_10_a7/
%G ru
%F IVM_1998_10_a7
B. A. Kats. Integration over a~plane fractal curve, a~jump problem and generalized measures. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (1998), pp. 53-65. http://geodesic.mathdoc.fr/item/IVM_1998_10_a7/

[1] Mandelbrot B. B., The fractal geometry of nature, Freeman, San Francisco, 1982 | MR | Zbl

[2] Feder E., Fraktaly, Mir, M., 1991, 260 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 Univ. Math. J., 40:2 (1991), 567–594 | DOI | MR | Zbl

[5] Harrison J., “Stokes' theorem for nonsmooth chains”, Bull. Amer. Math. Soc., 29:2 (1993), 235–242 | DOI | MR | Zbl

[6] Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973, 342 pp. | MR

[7] Harrison J., Norton A., “The Gauss–Green theorem for fractal boundaries”, Duke Math. J., 67:3 (1992), 575–586 | DOI | MR

[8] Kats B. A., “Ob integrirovanii po nespryamlyaemoi krivoi”, Vopr. mat., mekh. splosh. sred i primeneniya mat. metodov v str-ve, MISI, M., 1992, 63–69

[9] Kats B. A., “Ob odnoi versii kraevoi zadachi Rimana na fraktalnoi krivoi”, Izv. vuzov. Matematika, 1994, no. 4, 10–20 | MR | Zbl

[10] Jonssen A., Wallin H., “Function spaces on subsets of $\mathbb{R}$”, Math. Reports, 2, no. 1, Harwood Acad. Publ., London, 1984

[11] Ob'edkov T. E., “Primenenie nestandartnogo analiza k teorii integrirovaniya i reshenie zadachi Rimana o skachke”, Tez. dokl. mezhdunar. konf. “Algebra i analiz”, Ch. II, Kazan, 1994, 96–97

[12] Khermander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, T. 1, Mir, M., 1986, 462 pp.

[13] Dynkin E. M., “Gladkost integralov tipa Koshi”, Zap. nauchn. semin. LOMI AN SSSR, 92, 1979, 115–133 | MR

[14] Gakhov F. D., Kraevye zadachi, 3-e izd., Nauka, M., 1977, 640 pp. | MR

[15] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, 3-e izd., ispr. i dop., Nauka, M., 1968, 511 pp. | MR

[16] Kats B. A., “Zadacha Rimana na zamknutoi zhordanovoi krivoi”, Izv. vuzov. Matematika, 1983, no. 4, 68–80 | MR | Zbl

[17] Kats B. A., “Zadacha Rimana na razomknutoi zhordanovoi krivoi”, Izv. vuzov. Matematika, 1983, no. 12, 30–38 | MR | Zbl

[18] Markushevich A. I., Izbrannye glavy teorii analiticheskikh funktsii, Nauka, M., 1976, 191 pp. | MR | Zbl

[19] Dolzhenko E. P., “O “stiranii” osobennostei analiticheskikh funktsii”, UMN, 18:4 (1963), 135–142 | MR | Zbl

[20] Gamelin T. V., Ravnomernye algebry, Mir, M., 1973, 334 pp. | Zbl

[21] Vekua I. N., Obobschennye analiticheskie funktsii, 2-e izd., pererab., Nauka, M., 1988, 509 pp. | MR | Zbl

[22] Väisälä J., Vuorinen M., Wallin H., Thick sets and quasi-symmetric maps, Preprint 2. Reports of Dept of Math., Univ. of Helsinki, 1992, 25 pp.

[23] Kheiman U., Kennedi P., Subgarmonicheskie funktsii, T. 1, Mir, M., 1980, 304 pp.