Geodesic
Metric Characteristics of Non-Rectifiable Arcs and the Jump Problem
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 150 (2008) no. 1, pp. 56-64

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The paper is dealing with the boundary value problem on reconstruction of holomorphic function with known jump on a given non-rectifiable arc. There are introduced new metric characteristics of dimensional type for the non-rectifiable arcs. The main result of the paper is new condition for solvability of the jump problem in terms of the mentioned characteristics. It improves the known conditions of that kind.
Keywords: holomorphic function, the jump problem
Mots-clés : non-rectifiable arc, fractional dimension. 
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     author = {B. A. Kats},
     title = {Metric {Characteristics} of {Non-Rectifiable} {Arcs} and the {Jump} {Problem}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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     publisher = {mathdoc},
     volume = {150},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2008_150_1_a4/}
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B. A. Kats. Metric Characteristics of Non-Rectifiable Arcs and the Jump Problem. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 150 (2008) no. 1, pp. 56-64. http://geodesic.mathdoc.fr/item/UZKU_2008_150_1_a4/