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...- Invarianten bei verallgemeinerten Carlesonmengen.

Monatshefte für Mathematik

$𝐇$-valued differential forms on $𝐇$

Proceedings of the 11th Winter School on Abstract Analysis

3x+1 inverse orbit generating functions almost always have natural boundaries

Acta Arithmetica

The 3x+k function ${T}_{k}\left(n\right)$ sends n to (3n+k)/2, resp. n/2, according as n is odd, resp. even, where k ≡ ±1 (mod 6). The map ${T}_{k}\left(·\right)$ sends integers to integers; for m ≥1 let n → m mean that m is in the forward orbit of n under iteration of ${T}_{k}\left(·\right)$. We consider the generating functions ${f}_{k,m}\left(z\right)={\sum }_{n>0,n\to m}{z}^{n}$, which are holomorphic in the unit disk. We give sufficient conditions on (k,m) for the functions ${f}_{k,m}\left(z\right)$ to have the unit circle |z|=1 as a natural boundary to analytic continuation. For the 3x+1 function these conditions hold for all m...

517.53

Matematiceskij sbornik

5-dissections and sign patterns of Ramanujan's parameter and its companion

Czechoslovak Mathematical Journal

In 1998, Michael Hirschhorn discovered the 5-dissection formulas of the Rogers-Ramanujan continued fraction $R\left(q\right)$ and its reciprocal. We obtain the 5-dissections for functions $R\left(q\right)R{\left({q}^{2}\right)}^{2}$ and $R{\left(q\right)}^{2}/R\left({q}^{2}\right)$, which are essentially Ramanujan’s parameter and its companion. Additionally, 5-dissections of the reciprocals of these two functions are derived. These 5-dissection formulas imply that the coefficients in their series expansions have periodic sign patterns with few exceptions.

A bound for reflections across Jordan curves.

Georgian Mathematical Journal

A boundary value problem for Beltrami differential equation

Banach Center Publications

Solutions to Beltrami differential equation with prescribed boundary correspondence in some plane domains are given.

A boundary value problem for Hermitian monogenic functions.

Boundary Value Problems [electronic only]

A brief overview of Fornberg-like methods for conformal mapping of simply and multiply connected regions.

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

$ACL$ and differentiability of $Q$-homeomorphisms.

Annales Academiae Scientiarum Fennicae. Mathematica

A Cantor regular set which does not have Markov's property

Annales Polonici Mathematici

A Cauchy-Pompeiu formula in super Dunkl-Clifford analysis

Czechoslovak Mathematical Journal

Using a distributional approach to integration in superspace, we investigate a Cauchy-Pompeiu integral formula in super Dunkl-Clifford analysis and several related results, such as Stokes formula, Morera's theorem and Painlevé theorem for super Dunkl-monogenic functions. These results are nice generalizations of well-known facts in complex analysis.

A cellular parametrization for closed surfaces with a distinguished point.

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

A certain class of analytic and multivalent functions defined by means of a linear operator.

JIPAM. Journal of Inequalities in Pure &amp; Applied Mathematics [electronic only]

A characterisation of plane quasiconformal maps using triangles

Publicacions Matemàtiques

A characteristic property of orthogonal pencils of coaxal circles from the standpoint of conformal mapping

Annales Polonici Mathematici

A characterization of BMO and $BM{O}_{\varrho }$

Studia Mathematica

A characterization of damped and undamped harmonic oscillations by a superposition property II.

Mathematica Pannonica

A characterization of Fuchsian groups acting on complex hyperbolic spaces

Czechoslovak Mathematical Journal

Let $G\subset \mathrm{𝐒𝐔}\left(2,1\right)$ be a non-elementary complex hyperbolic Kleinian group. If $G$ preserves a complex line, then $G$ is $ℂ$-Fuchsian; if $G$ preserves a Lagrangian plane, then $G$ is $ℝ$-Fuchsian; $G$ is Fuchsian if $G$ is either $ℂ$-Fuchsian or $ℝ$-Fuchsian. In this paper, we prove that if the traces of all elements in $G$ are real, then $G$ is Fuchsian. This is an analogous result of Theorem V.G. 18 of B. Maskit, Kleinian Groups, Springer-Verlag, Berlin, 1988, in the setting of complex hyperbolic isometric groups. As an application...

A characterization of lines among Lipschitz graphs.

Mathematische Annalen

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