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Geometric properties of Wright function

Sudhananda Maharana, Jugal K. Prajapat, Deepak Bansal (2018)

Mathematica Bohemica

In the present paper, we investigate certain geometric properties and inequalities for the Wright function and mention a few important consequences of our main results. A nonlinear differential equation involving the Wright function is also investigated.

Geometric rigidity of conformal matrices

Daniel Faraco, Xiao Zhong (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We provide a geometric rigidity estimate à la Friesecke-James-Müller for conformal matrices. Namely, we replace SO ( n ) by an arbitrary compact set of conformal matrices, bounded away from 0 and invariant under SO ( n ) , and rigid motions by Möbius transformations.

Good metric spaces without good parameterizations.

Stephen Semmes (1996)

Revista Matemática Iberoamericana

A classical problem in geometric topology is to recognize when a topological space is a topological manifold. This paper addresses the question of when a metric space admits a quasisymmetric parametrization by providing examples of spaces with many Eucledian-like properties which are nonetheless substantially different from Euclidean geometry. These examples are geometrically self-similar versions of classical topologically self-similar examples from geometric topology, and they can be realized...

Good-irreducible inner functions on a polydisc

Eric T. Sawyer (1979)

Annales de l'institut Fourier

An explicit formula is developed for Nevanlinna class functions whose behaviour at the boundary is “sufficiently rational” and is then used to deduce the uniqueness of the factorization of such inner functions. A generalization of a theorem of Frostman is given and the above results are then applied to the construction of good and/or irreducible inner functions on a polydisc.

Green functions for killed random walks in the Weyl chamber of Sp(4)

Kilian Raschel (2011)

Annales de l'I.H.P. Probabilités et statistiques

We consider a family of random walks killed at the boundary of the Weyl chamber of the dual of Sp(4), which in addition satisfies the following property: for any n ≥ 3, there is in this family a walk associated with a reflection group of order 2n. Moreover, the case n = 4 corresponds to a process which appears naturally by studying quantum random walks on the dual of Sp(4). For all the processes belonging to this family, we find the exact asymptotic of the Green functions along all infinite paths...

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