Premium
On the solution of the triple correlation equation
Author(s) -
v. Wolfersdorf L.
Publication year - 2003
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310092
Subject(s) - mathematics , bounded function , functional equation , integro differential equation , fisher's equation , transformation (genetics) , mathematical analysis , summation equation , fourier transform , function (biology) , variable (mathematics) , integral equation , matrix difference equation , riccati equation , partial differential equation , chemistry , biochemistry , evolutionary biology , biology , gene
The paper presents an analytic treatment of the triple correlation equation which occurs in spectroscopy. By means of the Fourier transformation the nonlinear integral equation is reduced to a functional equation in two variables. For the solvability of this functional equation necessary and sufficient conditions are derived and the complex‐valued solution of the equation is given in closed form. Thereby the determination of the argument of the solution function (the phase) is carried out with the aid of the bounded solution to a related functional equation in a single variable.