1995/08/28 by H. W. Braden, V. M. Buchstaber, Victor Matveevich Buchstaber +2
Mathematics · Physics and Astronomy · #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Nonlinear Waves and Solitons #Operator Algebras (math.OA) #Quantum Mechanics and Non-Hermitian Physics #funct-an #math.OA
paper · pdf · doi:10.48550/arxiv.funct-an/9508002
26 pages latex2e. A further example is included
openalex publication_date 1995/08/28 · arxiv created 1996/04/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The general analytic solution to the functional equation ϕ1(x+y)= \biggl|\matrixϕ2(x)ϕ2(y)\crϕ3(x)ϕ3(y)\cr\biggr| \over \biggl|\matrixϕ4(x)ϕ4(y)\crϕ5(x)ϕ5(y)\cr\biggr| is characterised. Up to the action of the symmetry group, this is described in terms of Weierstrass elliptic functions. We illustrate our theory by applying it to the classical addition theorems of the Jacobi elliptic functions and the functional equations ϕ1(x+y)=ϕ4(x)ϕ5(y)+ϕ4(y)ϕ5(x) and Ψ1(x+y)=Ψ2(x+y) ϕ2(x)ϕ3(y) +Ψ3(x+y) ϕ4(x)ϕ5(y).