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I have some function $f$, real valued and continuous. I formed functions $\{f_{m,k}, k \in \mathbb{Z}, m>0\}$ such that that $\mathrm{span}\{f_{m,k}, k \in \mathbb{Z}, m>0\}$ is dense in $L_p(R)$.

Now I would like to constract a Riesz basis from $\{f_{m,k}, k \in \mathbb{Z}, m>0\}$, but unfortunately, my $\{f_{m,k}\}$ does not generate a Riesz basis.

I am wondering if there is some weaker/stronger structure than the Riesz basis, such that $\{f_{m,k}, k \in \mathbb{Z}, m>0\}$ can possibly generate?

Thank you.

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Maybe some kind of a frame? – user31373 Jul 2 '12 at 17:04
@Leonid Kovalev: Thank you. – Michael Jul 2 '12 at 17:43
up vote 0 down vote accepted

The term you're looking for is probably Schauder basis, altough for that you also need some independence properties (as usual with bases).

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