Page 1 Next

Displaying 1 – 20 of 163

Showing per page

Radial growth and variation of univalent functions and of Dirichlet finite holomorphic functions

Daniel Girela (1996)

Colloquium Mathematicae

A well known result of Beurling asserts that if f is a function which is analytic in the unit disc Δ = z : | z | < 1 and if either f is univalent or f has a finite Dirichlet integral then the set of points e i θ for which the radial variation V ( f , e i θ ) = 0 1 | f ' ( r e i θ ) | d r is infinite is a set of logarithmic capacity zero. In this paper we prove that this result is sharp in a very strong sense. Also, we prove that if f is as above then the set of points e i θ such that ( 1 - r ) | f ' ( r e i θ ) | o ( 1 ) as r → 1 is a set of logarithmic capacity zero. In particular, our results give...

Random perturbations of exponential Riesz bases in L 2 ( - π , π )

Gennadii Chistyakov, Yura Lyubarskii (1997)

Annales de l'institut Fourier

Let a sequence { λ n } be given such that the exponential system { exp ( i λ n x ) } forms a Riesz basis in L 2 ( - π , π ) and { ξ n } be a sequence of independent real-valued random variables. We study the properties of the system { exp ( i ( λ n + ξ n ) x ) } as well as related problems on estimation of entire functions with random zeroes and also problems on reconstruction of bandlimited signals with bandwidth 2 π via their samples at the random points { λ n + ξ n } .

Random polynomials and (pluri)potential theory

Thomas Bloom (2007)

Annales Polonici Mathematici

For certain ensembles of random polynomials we give the expected value of the zero distribution (in one variable) and the expected value of the distribution of common zeros of m polynomials (in m variables).

Random walks in ( + ) 2 with non-zero drift absorbed at the axes

Irina Kurkova, Kilian Raschel (2011)

Bulletin de la Société Mathématique de France

Spatially homogeneous random walks in ( + ) 2 with non-zero jump probabilities at distance at most 1 , with non-zero drift in the interior of the quadrant and absorbed when reaching the axes are studied. Absorption probabilities generating functions are obtained and the asymptotic of absorption probabilities along the axes is made explicit. The asymptotic of the Green functions is computed along all different infinite paths of states, in particular along those approaching the axes.

Currently displaying 1 – 20 of 163

Page 1 Next