In his paper, Huybrechs considered a

square-integrable function f [member of] [L.sup.2](-1,1) that is not necessarily smooth or periodic.

We point out that, following [12], the Hilbert space can be taken to be given by a pair of square-integrable functions on the real line.

It consists of square-integrable functions defined on the real line (see [22, 23] for details).

Here we construct a chaotic linear operator by "lifting" 2B to the space [L.sub.2] of square-integrable functions (more precisely to the Hilbert space [L.sub.2](0, [pi]) of 2[pi]-periodic odd functions).

The Hilbert space [L.sub.2](0, [pi]) of square-integrable functions is isomorphic with [l.sub.2] (by the Riesz-Fischer theorem) and is a natural functional representation of the sequence space [l.sub.2].

The previous constructions allow us the definition of fractal bases of the space of

square-integrable functions on I .

[c.sub.p]--specific heat, J/kgK; [e.sub.RMS]--root mean square error, K; [h.sub.c]--thermal contact conductance, W/[m.sup.2]K; H--Hilbert space of square-integrable functions; I--maximum number of parameters; k--thermal conductivity, W/mK; L--length, m; N--number of sensors; q--heat flux, W/[m.sup.2]; S--objective function, [K.sup.2]; t--time, s; [t.sub.f]--final time, s; T--temperature, K; [T.sub.0]--constant temperatures at specimens' end, K; [T.sub.i]--initial temperature, K; Y--measured temperatures, K; x--Cartesian spatial coordinate.

We are after the function [h.sub.c](t) over the whole time domain (0, [t.sub.f]), with the assumption that [h.sub.c](t) belongs to the Hilbert space of square-integrable functions in the time domain [13]--denoted as

A converse of the multi-band result for the classical case of continuous,

square-integrable functions is given in [3].

[L.sub.2]([Omega]) denotes the space of

square-integrable functions over [Omega] of [n.sub.sp] dimensions containing the function f having a finite [L.sub.2] norm of [[f]].