ROWE1.MWS

This MAPLE 6 worksheet displays Haar's first two sons and first two

daughters simultaneously. It also uses the spreadsheet

package to display the inner product of these siblings.

Author: Dr. E. Rowe

Department of Mathematics

North Carolina A & T State Univ.

Greensboro, NC 27411

rowee@ncat.edu

Date: 13 Nov. 2000

>

> restart;

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> phi := t -> piecewise(0 <= t and t < 1, 1);

>

> for n from 1 to 2 do

> for k from 0 to (2^n - 1) do

> phi||n||k := phi(2^n * t - k):

> phi||n||k := unapply(phi||n||k, t);

> end:

> end:

>

>

> with(plots):

```Warning, the name changecoords has been redefined
```

>

>

> psi||1||0 := t -> phi(4*t) - phi(4*t - 1);

> psi||1||1 := t -> phi(4*t - 2) - phi(4*t - 3);

>

> display(array(1..2,1..2,[[plot(phi||1||0(t),t=0..1, title=`Haar's First Son`), plot(phi||1||1(t), t=0..1, title=`Haar's Second Son`)],
[plot(psi||1||0(t),t=0..1, title=`Haar's First Daughter`), plot(psi||1||1(t), t=0..1, title=`Haar's Second Daughter`)]]));

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> innerProduct := proc(f, g,a,b)

> # f - function

> # g - function

> # a - beginning of interval

> # b - end of interval

> int(f(x)*g(x),x=a..b);

> #evalf(%);

> end;

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