Displaying similar documents to “The Ornstein-Uhlenbeck generator perturbed by the gradient of a potential”

Composition operators on Banach spaces of formal power series

B. Yousefi, S. Jahedi (2003)

Bollettino dell'Unione Matematica Italiana

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Let β n n = 0 be a sequence of positive numbers and 1 p < . We consider the space H p β of all power series f z = n = 0 f n z n such that n = 0 f n p β n p < . Suppose that 1 p + 1 q = 1 and n = 1 n q j β n q = for some nonnegative integer j . We show that if C φ is compact on H p β , then the non-tangential limit of φ j + 1 has modulus greater than one at each boundary point of the open unit disc. Also we show that if C φ is Fredholm on H p β , then φ must be an automorphism of the open unit disc.

Schwartz kernels on the Heisenberg group

Alessandro Veneruso (2003)

Bollettino dell'Unione Matematica Italiana

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Let H n be the Heisenberg group of dimension 2 n + 1 . Let L 1 , , L n be the partial sub-Laplacians on H n and T the central element of the Lie algebra of H n . We prove that the kernel of the operator m L 1 , , L n , - i T is in the Schwartz space S H n if m S R n + 1 . We prove also that the kernel of the operator h L 1 , , L n is in S H n if h S R n and that the kernel of the operator g L , - i T is in S H n if g S R 2 . Here L = L 1 + + L n is the Kohn-Laplacian on H n .

On the range of elliptic operators discontinuous at one point

Cristina Giannotti (2002)

Bollettino dell'Unione Matematica Italiana

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Let L be a second order, uniformly elliptic, non variational operator with coefficients which are bounded and measurable in R d ( d 3 ) and continuous in R d 0 . Then, if Ω R d is a bounded domain, we prove that L W 2 , p Ω is dense in L p Ω for any p 1 , d / 2 .

Global existence and regularity of solutions for complex Ginzburg-Landau equations

Stéphane Descombes, Mohand Moussaoui (2000)

Bollettino dell'Unione Matematica Italiana

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Si considerano equazioni di Ginzburg-Landau complesse del tipo u t - α Δ u + P u 2 u = 0 in R N dove P è polinomio di grado K a coefficienti complessi e α è un numero complesso con parte reale positiva α . Nell'ipotesi che la parte reale del coefficiente del termine di grado massimo P sia positiva, si dimostra l'esistenza e la regolarità di una soluzione globale nel caso α < C α , dove C dipende da K e N .