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A characterization of space-filling curves.

Gaspar Mora, Juan A. Mira (2002)

RACSAM

En este artículo revisamos un famoso teorema, descubierto por H. Steinhaus en 1936, en el que se da una condición suficiente que permite obtener las funciones coordenadas de una curva que llena el cuadrado unidad. Ponemos de manifiesto que el recíproco de este teorema no se cumple para la curva de Lebesgue. Aquí proponemos un teorema de caracterización de curvas que llenan el espacio, basado en una condición de llenado. Asimismo, damos una caracterización constructiva de esta condición de llenado...

A comparative analysis of Bernstein type estimates for the derivative of multivariate polynomials

Szilárd Gy. Révész (2006)

Annales Polonici Mathematici

We compare the yields of two methods to obtain Bernstein type pointwise estimates for the derivative of a multivariate polynomial in a domain where the polynomial is assumed to have sup norm at most 1. One method, due to Sarantopoulos, relies on inscribing ellipses in a convex domain K. The other, pluripotential-theoretic approach, mainly due to Baran, works for even more general sets, and uses the pluricomplex Green function (the Zaharjuta-Siciak extremal function). When the inscribed ellipse method...

A comparison of three recent selection theorems

Caterina Maniscalco (2007)

Mathematica Bohemica

We compare a recent selection theorem given by Chistyakov using the notion of modulus of variation, with a selection theorem of Schrader based on bounded oscillation and with a selection theorem of Di Piazza-Maniscalco based on bounded 𝒜 , Λ -oscillation.

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