Espaces de Bargmann généralisés et formules explicites pour leurs noyaux reproduisants

On products of some Toeplitz operators on polyanalytic Fock spaces

“…Basic informations about polyanalytic functions can be found in the book [4]. The reproducing kernel of the Hilbert space F 2 α,n has been computed using various method (see for instance [1], [3] or [7]). It can be written as…”

The hyperbolic-type point process

“…In particular, it was proved there that (5) V 1 0 (N r ) = r 2 1 − r 4 , and another proof of this result is given in [4]. However, beware that the Gaussian analytic series in the disc studied in [4] are in general not determinantal and that asymptotic formulas for the variance of N r are derived there from a formula quite similar to (2). More generally, the adaptation of our previous proof of Shirai's result yields the following formula for V ν m (N r ): Proposition 2.…”

“…and recall the hyperbolic distance: d(z, w)) . 2 Unlike the Euclidean setting, the strength ν of the magnetic field can not be reduced to one.…”

Analysis of generalized Poisson distributions associated with higher Landau levels

“…This is a self-adjoint operator in the Hilbert space L 2 (C, e −|z| 2 dz) where dz is the Lebesgue measure in C and has purely discrete positive spectrum given by the set of nonnegative integers ( [2]). Actually, the direct sum decomposition holds…”