...- Invarianten bei verallgemeinerten Carlesonmengen.
-valued differential forms on
3x+1 inverse orbit generating functions almost always have natural boundaries
The 3x+k function sends n to (3n+k)/2, resp. n/2, according as n is odd, resp. even, where k ≡ ±1 (mod 6). The map sends integers to integers; for m ≥1 let n → m mean that m is in the forward orbit of n under iteration of . We consider the generating functions , which are holomorphic in the unit disk. We give sufficient conditions on (k,m) for the functions 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
5-dissections and sign patterns of Ramanujan's parameter and its companion
In 1998, Michael Hirschhorn discovered the 5-dissection formulas of the Rogers-Ramanujan continued fraction and its reciprocal. We obtain the 5-dissections for functions and , 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.
A boundary value problem for Beltrami differential equation
Solutions to Beltrami differential equation with prescribed boundary correspondence in some plane domains are given.
A boundary value problem for Hermitian monogenic functions.
A brief overview of Fornberg-like methods for conformal mapping of simply and multiply connected regions.
and differentiability of -homeomorphisms.
A Cantor regular set which does not have Markov's property
A Cauchy-Pompeiu formula in super Dunkl-Clifford analysis
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.
A certain class of analytic and multivalent functions defined by means of a linear operator.
A characterisation of plane quasiconformal maps using triangles
A characteristic property of orthogonal pencils of coaxal circles from the standpoint of conformal mapping
A characterization of BMO and
A characterization of damped and undamped harmonic oscillations by a superposition property II.
A characterization of Fuchsian groups acting on complex hyperbolic spaces
Let be a non-elementary complex hyperbolic Kleinian group. If preserves a complex line, then is -Fuchsian; if preserves a Lagrangian plane, then is -Fuchsian; is Fuchsian if is either -Fuchsian or -Fuchsian. In this paper, we prove that if the traces of all elements in are real, then 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.