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- Author or Editor: Péter László x
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The ancient constitution of Hungary consisted of the mutually recognised rights and obligations of two actors: the Crown and the nobility. The reformers aimed at creating a Hungarian civil society through legislation. Conversion meant the replacement of the constitution, based on rights, by another system, based on statute laws. The April Laws broke the back of the old social order based on hereditary right and laid the foundation of the new Hungary.
Abstract
The aim of this paper is to continue our investigations started in [15], where we studied the summability of weighted Lagrange interpolation on the roots of orthogonal polynomials with respect to a weight function w. Starting from the Lagrange interpolation polynomials we constructed a wide class of discrete processes which are uniformly convergent in a suitable Banach space (C ρ, ‖‖ρ) of continuous functions (ρ denotes (another) weight). In [15] we formulated several conditions with respect to w, ρ, (C ρ, ‖‖ρ) and to summation methods for which the uniform convergence holds. The goal of this part is to study the special case when w and ρ are Freud-type weights. We shall show that the conditions of results of [15] hold in this case. The order of convergence will also be considered.
Abstract
Starting from the Lagrange interpolation on the roots of Jacobi polynomials, a wide class of discrete linear processes is constructed using summations. Some special cases are also considered, such as the Fejr, de la Valle Poussin, Cesro, Riesz and Rogosinski summations. The aim of this note is to show that the sequences of this type of polynomials are uniformly convergent on the whole interval [-1,1] in suitable weighted spaces of continuous functions. Order of convergence will also be investigated. Some statements of this paper can be obtained as corollaries of our general results proved in [15].
Abstract
We investigate the repeated and sequential portfolio St. Petersburg games. For the repeated St. Petersburg game, we show an upper bound on the tail distribution, which implies a strong law for a truncation. Moreover, we consider the problem of limit distribution. For the sequential portfolio St. Petersburg game, we obtain tight asymptotic results for the growth rate of the game.
