Newcomer's question

[Stefan Stoll]

Dear All,

I am a physical chemist working in the field of magnetic
resonance. The following problem seems to be solvable by
geometric computations:

  Given three functions B,L and W over some closed subregion K
  over (theta,phi) where theta=0..pi and phi=0..2*pi, calculate
  the distribution of function B values weighted by W and
  "broadened" by L.
  Let w be a point of K. L(w) is a scalar and defines the width
  of a Gaussian distribution with which the distribution of B
  values of an infinitesimal region dK around w have to be
  convoluted (in the Fourier sense).

If the domain of the function was 1D, the problem would be easy
to solve, since the requested distribution can be obtained starting
from  B's inverse function's first derivative.

Three more remarks:
- The function B can only be evaluated numerically over a grid
  covering the region K. It may have a couple of minima and
  maxima, but is well-behaved (smooth, continuous and differentiable).
- Using contouring methods is possible for the problem if L is
  constant over K. But unfortunately it is not.

I hope I was clear enough. Any suggestions extremely welcome!

  Stefan

--
Stefan Stoll                Fon [41](1) 632 61 39
Physical Chemistry Lab      Fax [41](1) 632 10 21
ETH Zurich, Switzerland     E-mail stoll at phys.chem.ethz.ch

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