I. Wavelet calculations.
 II. Calculation of approximation spaces in one dimension.
 III. Calculation of approximation spaces in one dimension II.
 IV. One dimensional problems.
 V. Stochastic optimization in one dimension.
 VI. Scalar product in N-dimensions.
 VII. Wavelet transform of payoff function in N-dimensions.
 1 Separation of variables for payoff function.
 VIII. Solving N-dimensional PDEs.

## Wavelet transform of payoff function in N-dimensions.

e use setup and notation of the section ( Scalar product in N dimensions ).

We introduce the notation for the function being the -projection of on .

 1 Separation of variables for payoff function.