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Displaying similar documents to “An extension of the Riemann-Lebesgue lemma and some applications.”

Compactifications, Hartman functions and (weak) almost periodicity

Gabriel Maresch, Reinhard Winkler

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We investigate Hartman functions on a topological group G. Recall that (ι,C) is a group compactification of G if C is a compact group, ι: G → C is a continuous group homomorphism and ι(G) ⊆ C is dense. A bounded function f: G → ℂ is a Hartman function if there exists a group compactification (ι,C) and F: C → ℂ such that f = F∘ι and F is Riemann integrable, i.e. the set of discontinuities of F is a null set with respect to the Haar measure. In particular, we determine how large a compactification...

Riemann problem on the double of a multiply connected circular region

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.

The Basic Existence Theorem of Riemann-Stieltjes Integral

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...

A family of deformations of the Riemann xi-function

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.

Riemann-Stieltjes Integral

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],...

Riemann mapping theorem in ℂⁿ

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

A strengthening of the Nyman-Beurling criterion for the Riemann hypothesis

Luis Báez-Duarte (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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According to the well-known Nyman-Beurling criterion the Riemann hypothesis is equivalent to the possibility of approximating the characteristic function of the interval 0 , 1 in mean square norm by linear combinations of the dilations of the fractional parts 1 / a ⁢ x for real a greater than 1 . It was conjectured and established here that the statement remains true if the dilations are restricted to those where the a ’s are positive integers. A constructive sequence of such approximations is given. ...

Solutions of Riemann–Weber type half-linear differential equation

Ondřej Došlý (2017)

Archivum Mathematicum

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We establish an asymptotic formula for a pair of linearly independent solutions of the subcritical Riemann–Weber type half-linear differential equation. We also complement the results of the author and M. Ünal, Acta Math. Hungar. 120 (2008), 147–163, where the equation was considered in the critical case.

Naturphilosophie and its role in Riemann’s mathematics

Umberto Bottazzini, Rossana Tazzioli (1995)

Revue d'histoire des mathématiques

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This paper sets out to examine some of Riemann’s papers and notes left by him, in the light of the “philosophical” standpoint expounded in his writings on . There is some evidence that many of Riemann’s works, including his of 1854 on the foundations of geometry, may have sprung from his attempts to find a unified explanation for natural phenomena, on the basis of his model of the ether.