docs/source/volume.rst: Explicit HT convention

Explicitly state the convention used for the harmonic transform operators and clearly state the difference between the convention used in HEALPix and NIFTy.

docs/source/volume.rst

@@ -211,3 +211,18 @@ Consequently, the inverse covariance operator will automatically have lower indi
 ensuring that the whole log-likelihood expression does not scale with resolution.
 **This upper-lower index convention is not coded into NIFTy**, in order to not reduce user freedom.
 One should however have this in mind when constructing log-likelihoods in order to ensure resolution independence.
+
+Harmonic Transform Convention
+.............................
+
+In NIFTy the convention for the harmonic transformations is set by requiring the zero mode of the transformed field to be the integral over the original field.
+This choice is convenient for the Fourier transformation and used throughout the literature.
+Note that for the spherical harmonics this convention is only rarely used and might result in unexpected factors in the transformed field.
+
+To be specific, for the spherical harmonics transformation this means that a monopole of unit amplitude in position-space which is transformed to the spherical harmonics domain and back to the original position space via the adjoint transformation will have a non-unit amplitude afterwards.
+The factor between the input field and the twice transformed field is :math:`1/4\pi`.
+In comparison to the convention used in HEALPix, this corresponds to dividing the output of the HEALPix transformed field by :math:`\sqrt{4\pi}` in each transformation.
+
+Depending on the use-case, additional volume factors must be accounted for.
+This is especially true if one wants to define the inverse transformation.
+Note that the convention for the harmonic transformations used in NIFTy results in non-unitary operators.