We study the spectral properties of Jabobi matrices. By combining Killip’s technique [13] with the technique of Killip and Simon [12] we obtain a result relating the properties of the elements of Jacobi matrices and the corresponding spectral measures. This theorem is a natural extension of a recent result of Laptev-Naboko-Safronov [17]. The author contemplated this paper as a part of an update...

Let R be a root system of type BC in a = Rr of general positive multiplicity. We introduce certain canonical weight function on Rr which in the case of symmetric domains corresponds to the integral kernel of the Berezin transform. We compute its spherical transform and prove certain Bernstein-Sato type formula. This generalizes earlier work of Unterberger-Upmeier, van Dijk-Pevsner, Neretin and ...

Let a,ß > -1 and Pla'3)(x) = (l-x)a(l+x)ßp[a'a){x), where Pjf (x) is the Jacobi function of the first kind, A > —(a + ß + l)/2, and -1 < i < 1. Let r the integral exists. It is known that for a + •>-Ä4r'<",')(*-i),£Ä<-> *J o whenever ß = 0, we have /(*) = lim 4 f fC« (x l) PÍÍ$A-*)\ . . r2(A + i/2) X sin 7rA^-:-L_¡-d\ w in J, r(A-ra + l/2)F(A + ^ + l/2) almost everywhere in [—1,1], In this pape...

Article history: Received 12 April 2008 Received in revised form 21 August 2008 Accepted 25 August 2008 Available online 5 September 2008

We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and Jacobi structures (canonical structures) associated with Lie algebroids and Jacobi algebroids. MSC 2000: 17B62 17B66 53D10 53D17