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Zap. Nauchn. Sem. POMI, 2017, Volume 458, Pages 31–41 (Mi znsl6452)  

Modules of families of vector measures on a Riemann surface

Yu. V. Dymchenkoa, V. A. Shlykb

a Far Eastern Federal University, Vladivostok, Russia
b Vladivostok Branch of Russian Customs Academy, Vladivostok, Russia

Abstract: We consider a Riemann surface in the broad sense of the term in the Hurwitz–Courant terminology and an open set with a compact closure on this surface. In this paper, it is established that a family of vector measures can be associated with a condenser on a given open set, following the Aikawa–Ohtsuka, whose modules are calculated directly with the help of a weighted capacity (with Muckenhoupt weight) of the given condenser.

Key words and phrases: modulus of curves famify, condenser capacity, Riemann surface, Muckenhoupt weight.

Full text: PDF file (186 kB)
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UDC: 517.5
Received: 14.09.2017

Citation: Yu. V. Dymchenko, V. A. Shlyk, “Modules of families of vector measures on a Riemann surface”, Analytical theory of numbers and theory of functions. Part 33, Zap. Nauchn. Sem. POMI, 458, POMI, St. Petersburg, 2017, 31–41

Citation in format AMSBIB
\Bibitem{DymShl17}
\by Yu.~V.~Dymchenko, V.~A.~Shlyk
\paper Modules of families of vector measures on a~Riemann surface
\inbook Analytical theory of numbers and theory of functions. Part~33
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 458
\pages 31--41
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6452}


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