Open AccessFourier transformation in spherical systems as a tool of structural biology
Author(s) -
A. V. Batyanovskii,
В. А. Намиот,
И. В. Филатов,
V. G. Tumanyan,
Esipova Ng,
I. D. Volotovsky
Publication year - 2020
Publication title -
vescì nacyânalʹnaj akadèmìì navuk belarusì. seryâ fìzìka-matèmatyčnyh navuk
Language(s) - English
Resource type - Journals
eISSN - 2524-2415
pISSN - 1561-2430
DOI - 10.29235/1561-2430-2020-56-4-496-503
Subject(s) - superposition principle , fourier transform , decomposition , fourier series , correctness , representation (politics) , transformation (genetics) , coordinate system , fourier analysis , discrete fourier series , mathematical analysis , mathematics , physics , algebra over a field , pure mathematics , algorithm , geometry , chemistry , fractional fourier transform , law , gene , biochemistry , organic chemistry , politics , political science
Applications of the most common adaptation of Fourier analysis in spherical coordinate systems used to solve a number of problems in structural biology, namely, flat wave decomposition (flat waves are represented as spherical functions decomposition), are herein considered. Arguments in favor of this decomposition are compared with other decompositions in superposition of special functions. A more general justification for the correctness of this decomposition is obtained than that existing today. A method for representing groups of atoms in the form of a Fourier object is proposed. It is also considered what opportunities give such a representation. The prospects for the application of Fourier analysis in structural biophysics are discussed.