Tommi H?yn?l?nmaa
Jul28-04, 11:11 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\nDo the interpolating wavelets (of degree m) form a Riesz basis of L^2(R) ?\nIf they do, what are the values of coefficients a and b in\n\na ||u||^2 <= \\sum_n |<u, e_n>|^2 <= b ||u||^2\n\n\nInterpolating wavelets are a biorthogonal wavelet family.\nTheir definition is given, for example, in\n\nS. Goedecker: Wavelets and their application for the solution of partial\ndifferential equations in physics\n\nFor interpolating wavelets, the dual scaling function is the Dirac delta\nfunction\n\nphidual( x ) = delta( x )\n\nand consequently the dual-h filter is\n\nht_j = delta_{j,0}.\n\nBTW, since the dual scaling function is not in L^2(R) the standard\nformalism of multiresolution analysis cannot be used as such. Does anyone\nknow a good reference for the MRA for this case?\n\n- Tommi Höynälänmaa -\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>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 -
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 -