There is no way around it: each theory rests on a tiny set of foundational propositions. Standard economics rests on behavioral axioms. After a long intellectual detour it should be clear by now that behavioral axioms are the wrong formal departure point. Being beyond repair, they have to be...

Real-time signal extraction (RTSE) concerns the determination of optimal asymmetric filters towards the end of a time series where - otherwise desirable - symmetric filters cannot be applied anymore. The attractiveness of this particular estimation problem resides in the generality of its scope....

We introduce the notions of elementary reducing subspaces and elementary irreducible-invariant subspaces—generated from wandering vectors—of a shift operator of countably infinite multiplicity, defined on a separable Hilbert space H. Necessary and sufficient conditions for a set of shift...

We show that, with respect to an orthonormal wavelet ψ(·)∈L2(R) any f(·)∈L2(R) is, on the one hand, the sum of its “layers of details” over all time-shifts, and on the other hand, the sum of its layers of details over all scales. The latter is well known and is a consequence of a...