B. A. Kats, “Integration over a fractal curve and the jump problem”, Mat. Zametki, 64:4 (1998), 549–557; Math. Notes, 64:4 (1998), 476

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Matematicheskie Zametki, 1998, Volume 64, Issue 4, Pages 549–557
DOI: https://doi.org/10.4213/mzm1429 (Mi mzm1429)

This article is cited in 10 scientific papers (total in 10 papers)

Integration over a fractal curve and the jump problem

B. A. Kats

Kazan State Academy of Architecture and Construction

Full-text PDF (213 kB) Citations (10)

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DOI: https://doi.org/10.4213/mzm1429

Abstract: A definition of integration, i.e., a generalization of a functional of the form

u (z) \mapsto \int_{Γ} f (z) u (z) d z

$u(z)\mapsto\int_\Gamma f(z)u(z)dz$
to the case where

Γ

$\Gamma$ is a fractal curve on the complex plane and

f (z)

$f(z)$ (integration density) is a function defined on this curve is given. The existence and uniqueness of the integral with given density are examined.

Received: 17.07.1996
Revised: 20.11.1997

English version:
Mathematical Notes, 1998, Volume 64, Issue 4, Pages 476–482
DOI: https://doi.org/10.1007/BF02314628

Bibliographic databases:

UDC: 517.9

Language: Russian

Citation: B. A. Kats, “Integration over a fractal curve and the jump problem”, Mat. Zametki, 64:4 (1998), 549–557; Math. Notes, 64:4 (1998), 476–482

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm1429

https://doi.org/10.4213/mzm1429

https://www.mathnet.ru/eng/mzm/v64/i4/p549

This publication is cited in the following 10 articles:

Ilya Boykov, Vladimir Roudnev, Alla Boykova, “Regular, Singular and Hypersingular Integrals over Fractal Contours”, Mathematics, 11:23 (2023), 4752
Kats B.A., Katz D.B., “Curvilinear Integrals of Discontinuous Functions Over Nonrectifiable Paths and Riemann Boundary-Value Problem”, Math. Meth. Appl. Sci., 42:6 (2019), 1795–1803
Guseynov Y., “Integrable boundaries and fractals for H?lder classes; the Gauss?Green theorem”, Calc. Var. Partial Differ. Equ., 55:4 (2016), 103
Boris A. Kats, Recent Progress in Operator Theory and Its Applications, 2012, 137
B. A. Kats, “Metric dimensions, generalized integrations, cauchy transform, and riemann boundary-value problem on nonrectifiable arcs”, Journal of Mathematical Sciences, 189:1 (2013), 113–131
Abreu-Blaya, R, “A jump problem for beta-analytic functions in domains with fractal boundaries”, Revista Matematica Complutense, 23:1 (2010), 105
Kats B.A., “The Cauchy Integral Over Non-Rectifiable Paths”, Complex Analysis and Dynamical Systems III, Contemporary Mathematics Series, 455, eds. Agranovsky M., Bshouty D., Karp L., Reich S., Shoikhet D., Zalcman L., Amer Mathematical Soc, 2008, 183–196
Abreu-Blaya R., Bory-Reyes J., Pena-Pena D., “Jump problem and removable singularities for monogenic functions”, Journal of Geometric Analysis, 17:1 (2007), 1–13
Ricardo Abreu-Blaya, Juan Bory-Reyes, Dixan Peña-Peña, “Jump problem and removable singularities for monogenic functions”, J Geom Anal, 17:1 (2007)
B. A. Kats, “The Stieltjes integral along a fractal contour and some of its applications”, Russian Math. (Iz. VUZ), 44:10 (2000), 19–29

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Full-text PDF :	214
References:	58
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