Add to ORKG39 pagesWe study α-harmonic functions on the complement of the sphere and on the complement of the hyperplane in Euclidean spaces of dimension bigger than one, for 1<α<2. We describe the corresponding Hardy spaces and prove the Fatou theorem for α-harmonic functions. We also give explicit formulas for the Martin kernel of the complement of the sphere and for the harmonic measure, Green function and Martin kernel of the complement of the hyperplane for the symmetric α-stable Lévy processes. Some extensions for the relativistic α-stable processes are discussed
International audienceWe consider the random walks killed at the boundary of the quarter plane, with...
We study a family of differential operators Lα α ≥ 0 in the unit ball D of Cn with n ≥ 2 that gene...
Critical points of approximations of the Dirichlet energy à la Sacks-Uhlenbeck are known to converge...
We study α-harmonic functions on the complement of the sphere and on the complement of the hyperplan...
AbstractRecently it was shown in [P. Kim, Fatou's theorem for censored stable processes, Stochastic ...
16 pagesInternational audienceIt is well known that if $h$ is a nonnegative harmonic function in the...
AbstractRecently it was shown in [P. Kim, Fatou's theorem for censored stable processes, Stochastic ...
In the n(≧2)-dimensional Euclidean (ξ)=(ξ_1.…, ξ_n) space, let v (ξ) be a positive harmonic function...
AbstractWe study functions which are harmonic in the upper half space with respect to (−Δ)α/2, 0<α<2...
By classical Fatou type theorems in various setups, it is well-known that positive harmonic function...
2000 Mathematics Subject Classification: Primary 26A33; Secondary 47G20, 31B05We study a singular va...
We study potential theoretic properties of strictly α-stable processes whose Levy measure is compara...
We study potential theoretic properties of strictly α-stable processes whose Levy measure is compara...
In the n(≧2)-dimensional Euclidean (ξ)=(ξ_1.…, ξ_n) space, let v (ξ) be a positive harmonic function...
This paper studies the boundary behaviour of $\lambda$-polyharmonic functions for the simple random ...
International audienceWe consider the random walks killed at the boundary of the quarter plane, with...
We study a family of differential operators Lα α ≥ 0 in the unit ball D of Cn with n ≥ 2 that gene...
Critical points of approximations of the Dirichlet energy à la Sacks-Uhlenbeck are known to converge...
We study α-harmonic functions on the complement of the sphere and on the complement of the hyperplan...
AbstractRecently it was shown in [P. Kim, Fatou's theorem for censored stable processes, Stochastic ...
16 pagesInternational audienceIt is well known that if $h$ is a nonnegative harmonic function in the...
AbstractRecently it was shown in [P. Kim, Fatou's theorem for censored stable processes, Stochastic ...
In the n(≧2)-dimensional Euclidean (ξ)=(ξ_1.…, ξ_n) space, let v (ξ) be a positive harmonic function...
AbstractWe study functions which are harmonic in the upper half space with respect to (−Δ)α/2, 0<α<2...
By classical Fatou type theorems in various setups, it is well-known that positive harmonic function...
2000 Mathematics Subject Classification: Primary 26A33; Secondary 47G20, 31B05We study a singular va...
We study potential theoretic properties of strictly α-stable processes whose Levy measure is compara...
We study potential theoretic properties of strictly α-stable processes whose Levy measure is compara...
In the n(≧2)-dimensional Euclidean (ξ)=(ξ_1.…, ξ_n) space, let v (ξ) be a positive harmonic function...
This paper studies the boundary behaviour of $\lambda$-polyharmonic functions for the simple random ...
International audienceWe consider the random walks killed at the boundary of the quarter plane, with...
We study a family of differential operators Lα α ≥ 0 in the unit ball D of Cn with n ≥ 2 that gene...
Critical points of approximations of the Dirichlet energy à la Sacks-Uhlenbeck are known to converge...