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Orthogonalize in a discrete setting

I am trying to implement Orthogonalize in a particular scenario.

First, I have

f[z_,n_]:=Product[1+z Part[pts,m],{m,1,n-1}]

The z argument above will be taken from a list of complex numbers
which I named zees (which also has length L), so


I want to orthogonalize {f[z[1],n],f[z[2],n],f[z[3],n]} with respect
to the discrete inner product Sum[u[k] Conjugate[v[k]] Part[pts,k],{k,
1,L}] so I tried

Orthogonalize[Table[f[z[i],n],{i,1,L}],Sum[#1 #2 Part[pts,k],{k,

and other variations to no avail.

What is the proper way to pass the functions/vectors to be
orthgonalized in this setting? And then, what is the proper way to set
up the inner product function based on the former?

Thanks for any help,

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