Are interpolating wavelets a Riesz basis?

From: Tommi H?yn?l?nmaa (tommi.hoynalanmaa_at_iki.fi)
Date: 07/28/04 

Date: 28 Jul 2004 11:11:51 -0400

Do the interpolating wavelets (of degree m) form a Riesz basis of L^2(R) ?
If they do, what are the values of coefficients a and b in
 
  a ||u||^2 <= \sum_n |<u, e_n>|^2 <= b ||u||^2
 
 
Interpolating wavelets are a biorthogonal wavelet family.
Their definition is given, for example, in
 
  S. Goedecker: Wavelets and their application for the solution of partial
  differential equations in physics
 
For interpolating wavelets, the dual scaling function is the Dirac delta
function
 
  phidual( x ) = delta( x )
 
and consequently the dual-h filter is
 
  ht_j = delta_{j,0}.
 
BTW, since the dual scaling function is not in L^2(R) the standard
formalism of multiresolution analysis cannot be used as such. Does anyone
know a good reference for the MRA for this case?
 
     - Tommi Höynälänmaa -