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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2014, Volume 156, Book 4, Pages 31–38 (Mi uzku1278)  
This article is cited in 4 scientific papers (total in 4 papers)

New metric characteristics of non-rectifiable curves with applications

D. B. Kats

Kazan (Volga Region) Federal University, Kazan, Russia
Full-text PDF (439 kB) Citations (4)
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Abstract: In this paper, the author summarizes the concept of Marcinkiewicz exponents, introduced earlier. These exponents are in fact new metric characteristics for non-rectifiable flat curves. The generalization that is presented here is used to solve boundary-value problems for holomorphic functions in domains whose boundaries are non-rectifiable.
Keywords: metric characteristics, fractals, non-rectifiable curves, Marcinkiewicz exponents.
Received: 06.10.2014
Document Type: Article
UDC: 517.53/.55
Language: Russian
Citation: D. B. Kats, “New metric characteristics of non-rectifiable curves with applications”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 156, no. 4, Kazan University, Kazan, 2014, 31–38
Citation in format AMSBIB
\Bibitem{Kat14}
\by D.~B.~Kats
\paper New metric characteristics of non-rectifiable curves with applications
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2014
\vol 156
\issue 4
\pages 31--38
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1278}
Linking options:
  • https://www.mathnet.ru/eng/uzku1278
  • https://www.mathnet.ru/eng/uzku/v156/i4/p31
    • This publication is cited in the following 4 articles:
    1. D. B. Kats, “Integrirovanie po nespryamlyaemym krivym kak raspredelenie”, Materialy XVII Vserossiiskoi molodezhnoi shkoly-konferentsii «Lobachevskie chteniya-2018»,  23-28 noyabrya 2018 g., Kazan.  Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 176, VINITI RAN, M., 2020, 50–60  mathnet  crossref  mathscinet
    2. D. B. Katz, “Marcinkiewicz exponents and a boundary-value jump problem for Beltrami equation”, Russian Math. (Iz. VUZ), 61:6 (2017), 37–43  mathnet  crossref  isi
    3. B. A. Kats, D. B. Katz, “New solvability criterion for jump problem”, Bol. Soc. Mat. Mex., 22:2, SI (2016), 361–366  crossref  mathscinet  zmath  isi
    4. D. B. Katz, “Local and weighted Marcinkiewicz exponents with applications”, J. Math. Anal. Appl., 440:1 (2016), 74–85  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
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