Premium
Separation of variables and commuting operators
Author(s) -
Hainzl J.,
Kirchgässner K.
Publication year - 1979
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670010405
Subject(s) - mathematics , eigenfunction , separable space , separation of variables , operator (biology) , differential operator , set (abstract data type) , separation (statistics) , pure mathematics , differential equation , mathematical analysis , algebra over a field , partial differential equation , eigenvalues and eigenvectors , computer science , biochemistry , physics , chemistry , repressor , quantum mechanics , transcription factor , gene , programming language , statistics
For any differential operator L , separable in some coordinate system, we construct a set of commuting operators S i such that 1) each S i maps solutions of Lu = 0 into solutions, and 2) the separated solutions of Lu = 0 are simultaneous eigenfunctions of S i . Moreover, a certain description of the separable coordinate system by S i is possible. The paper generalizes results obtained by W. Miller and others on many equations of mathematical physics.