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Infinite dimensional linear groups with many G - invariant subspaces

Leonid Kurdachenko, Alexey Sadovnichenko, Igor Subbotin (2010)

Open Mathematics

Let F be a field, A be a vector space over F, GL(F, A) be the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dim F(B/Core G(B)) is finite. In the current article, we study linear groups G such that every subspace of A is either nearly G-invariant or almost G-invariant in the case when G is a soluble p-group where p = char F.

Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of Lévy processes

Patie Pierre (2009)

Annales de l'I.H.P. Probabilités et statistiques

We first characterize the increasing eigenfunctions associated to the following family of integro-differential operators, for any α, x>0, γ≥0 and fa smooth function on + , 𝐋 ( γ ) f ( x ) = x - α ( σ 2 x 2 f ' ' ( x ) + ( σ γ + b ) x f ' ( x ) + 0 f e - r x - f ( x ) e - r γ + x f ' ( x ) r 𝕀 { r 1 } ν ( d r ) ) , ( 0 . 1 ) where the coefficients b ,σ≥0 and the measure ν, which satisfies the integrability condition ∫0∞(1∧r2)ν(dr)<+∞, are uniquely determined by the distribution of a spectrally negative, infinitely divisible random variable, with characteristic exponent ψ. L(γ) is known to be the infinitesimal generator of a positive...

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