Displaying similar documents to “An approximate layering method for multi-dimensional nonlinear parabolic systems of a certain type”

On the theorem of Ivasev-Musatov. II

Thomas-William Korner (1978)

Annales de l'institut Fourier

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As in Part I [Annales de l’Inst. Fourier, 27-3 (1997), 97-113], our object is to construct a measure whose support has Lebesgue measure zero, but whose Fourier transform drops away extremely fast.

Integrability theorems for trigonometric series

Bruce Aubertin, John Fournier (1993)

Studia Mathematica

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We show that, if the coefficients (an) in a series a 0 / 2 + ∑ n = 1 ∞ a n c o s ( n t ) tend to 0 as n → ∞ and satisfy the regularity condition that ∑ m = 0 ∞ ∑ j = 1 ∞ [ ∑ n = j 2 m ( j + 1 ) 2 m - 1 | a n - a n + 1 | ] ² 1 / 2 < ∞ , then the cosine series represents an integrable function on the interval [-π,π]. We also show that, if the coefficients (bn) in a series ∑ n = 1 ∞ b n s i n ( n t ) tend to 0 and satisfy the corresponding regularity condition, then the sine series represents an integrable function on [-π,π] if and only if ∑ n = 1 ∞ | b n | / n < ∞ . These conclusions were previously known to hold under stronger restrictions on the sizes...

Fluctuations of brownian motion with drift.

Joseph G. Conlon, Peder Olsen (1999)

Publicacions Matemàtiques

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Consider 3-dimensional Brownian motion started on the unit sphere {|x| = 1} with initial density ρ. Let ρt be the first hitting density on the sphere {|x| = t + 1}, t &gt; 0. Then the linear operators T defined by T ρ = ρ form a semigroup with an infinitesimal generator which is approximately the square root of the Laplacian. This paper studies the analogous situation for Brownian motion with a drift , where is small in a suitable scale invariant norm.