Relations Between Bourlet Operators of the Specific Form
Since the three types H, M, D or Bourlet operators all satisfy more or less special forms of the multiplication theorem (2.16), it is to be expected that there exist various simple relations between them. We shall search for such relationships in the specific form only (it would be more satisfactory to derive relations directly from the multiplication theorems), and only in the case of two special function algebras. The first of these is the algebra of entire functions of one real variable. We do not touch upon the problem of whether other Bourlet operators exist in this algebra besides those of the specific form.
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