Generalized Hilbert Functions

Generalized Hilbert Functions

Let M be a finite module and let I be an arbitrary ideal over a Noetherian local ring. We define the generalized Hilbert function of I on M using the 0th local cohomology functor. We show that our definition re-conciliates with that of Ciupercă. By generalizing Singh’s formula (which holds in the case of λ(M/IM)<∞), we prove that the generalized Hilbert coefficients j0, . . . , jd−2 are preserv...

Generalized Frames in Hilbert Spaces

The Hilbert Transform Ofthe Generalized Laguerre and Hermiteweight Functions

Explicit formulae are given for the Hilbert transform Z R ? w(t)dt=(t ? x), where w is either the generalized Laguerre weight function w(t) = 0 if t 0, w(t) = t e ?t if 0 < t < 1, and > ?1, x > 0, or the Hermite weight function w(t) = e ?t 2 , ?1 < t < 1, and ?1 < x < 1. Furthermore, numerical methods of evaluation are discussed based on recursion, contour integration and saddle-point asymptoti...

Multipliers of generalized frames in Hilbert spaces

Generalized Hilbert Numerators