Displaying similar documents to “Almost sure asymptotic behaviour of the r -neighbourhood surface area of Brownian paths”

An application of fine potential theory to prove a Phragmen Lindelöf theorem

Terry J. Lyons (1984)

Annales de l'institut Fourier

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We give a new proof of a Phragmén Lindelöf theorem due to W.H.J. Fuchs and valid for an arbitrary open subset U of the complex plane: if f is analytic on U , bounded near the boundary of U , and the growth of j is at most polynomial then either f is bounded or U ⊃ { | z | > r } for some positive r and f has a simple pole.

On the powerful part of n 2 + 1

Jan-Christoph Puchta (2003)

Archivum Mathematicum

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We show that n 2 + 1 is powerfull for O ( x 2 / 5 + ϵ ) integers n ≤ x at most, thus answering a question of P. Ribenboim.

A generalization of a theorem of Erdös on asymptotic basis of order 2

Martin Helm (1994)

Journal de théorie des nombres de Bordeaux

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Let 𝒯 be a system of disjoint subsets of ℕ * . In this paper we examine the existence of an increasing sequence of natural numbers, A , that is an asymptotic basis of all infinite elements T j of 𝒯 simultaneously, satisfying certain conditions on the rate of growth of the number of representations 𝑟 𝑛 ( 𝐴 ) ; 𝑟 𝑛 ( 𝐴 ) : = ( 𝑎 𝑖 , 𝑎 𝑗 ) : 𝑎 𝑖 < 𝑎 𝑗 ; 𝑎 𝑖 , 𝑎 𝑗 ∈ 𝐴 ; 𝑛 = 𝑎 𝑖 + 𝑎 𝑗 , for all sufficiently large n ∈ T j and j ∈ ℕ * A theorem of P. Erdös is generalized.

Regularity of irregularities on a brownian path

Samuel James Taylor (1974)

Annales de l'institut Fourier

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On a standard Brownian motion path there are points where the local behaviour is different from the pattern which occurs at a fixed t 0 with probability 1. This paper is a survey of recent results which quantity the extent of the irregularities and show that the exceptional points themselves occur in an extremely regular manner.

Plurisubharmonic functions with logarithmic singularities

E. Bedford, B. A. Taylor (1988)

Annales de l'institut Fourier

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To a plurisubharmonic function u on C n with logarithmic growth at infinity, we may associate the Robin function ρ u ( z ) = lim sup λ → ∞ u ( λ z ) - log ( λ z ) defined on P n - 1 , the hyperplane at infinity. We study the classes L + , and (respectively) L p of plurisubharmonic functions which have the form u = log ( 1 + | z | ) + O ( 1 ) and (respectively) for which the function ρ u is not identically - ∞ . We obtain an integral formula which connects the Monge-Ampère measure on the space C n with the Robin function on P n - 1 . As an application we obtain a criterion...