On subspaces of Riemann-Otsuki space.
Nadj, Djerdji F. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
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Nadj, Djerdji F. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
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Xiannan Li (2009)
Acta Arithmetica
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Dinu, Liviu Florin, Dinu, Mariana Ileana (2004)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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V. V. Mityushev (1997)
Annales Polonici Mathematici
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The Riemann problem has been solved in [9] for an arbitrary closed Riemann surface in terms of the principal functionals. This paper is devoted to solution of the problem only for the double of a multiply connected region and can be treated as complementary to [9,1]. We obtain a complete solution of the Riemann problem in that particular case. The solution is given in analytic form by a Poincaré series.
Kazuhisa Nakasho, Keiko Narita, Yasunari Shidama (2016)
Formalized Mathematics
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In this article, the basic existence theorem of Riemann-Stieltjes integral is formalized. This theorem states that if f is a continuous function and ρ is a function of bounded variation in a closed interval of real line, f is Riemann-Stieltjes integrable with respect to ρ. In the first section, basic properties of real finite sequences are formalized as preliminaries. In the second section, we formalized the existence theorem of the Riemann-Stieltjes integral. These formalizations are...
N. Paul Schembari, Michael Schramm (1990)
Colloquium Mathematicae
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Keiko Narita, Kazuhisa Nakasho, Yasunari Shidama (2016)
Formalized Mathematics
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In this article, the definitions and basic properties of Riemann-Stieltjes integral are formalized in Mizar [1]. In the first section, we showed the preliminary definition. We proved also some properties of finite sequences of real numbers. In Sec. 2, we defined variation. Using the definition, we also defined bounded variation and total variation, and proved theorems about related properties. In Sec. 3, we defined Riemann-Stieltjes integral. Referring to the way of the article [7],...
Krzysztof Jarosz (2012)
Annales Polonici Mathematici
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The classical Riemann Mapping Theorem states that a nontrivial simply connected domain Ω in ℂ is holomorphically homeomorphic to the open unit disc 𝔻. We also know that "similar" one-dimensional Riemann surfaces are "almost" holomorphically equivalent. We discuss the same problem concerning "similar" domains in ℂⁿ in an attempt to find a multidimensional quantitative version of the Riemann Mapping Theorem
Masatoshi Suzuki (2013)
Acta Arithmetica
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We introduce a family of deformations of the Riemann xi-function endowed with two continuous parameters. We show that it has rich analytic structure and that its conjectural (mild) zero-free region for some fixed parameter is a sufficient condition for the Riemann hypothesis to hold for the Riemann zeta function.
Christoph Klein (1987)
Studia Mathematica
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H.F. Baker (1894)
Mathematische Annalen
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Ch. Klein, S. Rolewicz (1984)
Studia Mathematica
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Jean-Louis Nicolas (2012)
Acta Arithmetica
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Tibor Šalát (1987)
Mathematica Slovaca
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Roland Coghetto (2017)
Formalized Mathematics
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Some authors have formalized the integral in the Mizar Mathematical Library (MML). The first article in a series on the Darboux/Riemann integral was written by Noboru Endou and Artur Korniłowicz: [6]. The Lebesgue integral was formalized a little later [13] and recently the integral of Riemann-Stieltjes was introduced in the MML by Keiko Narita, Kazuhisa Nakasho and Yasunari Shidama [12]. A presentation of definitions of integrals in other proof assistants or proof checkers (ACL2, COQ,...