Journal of Lie Theory

no. 2
Nonabelian Harmonic Analysis and Functional Equations on Compact Groups
Journal of Lie Theory, Volume 21 (2011) no. 2, pp. 427-456
Making use of nonabelian harmonic analysis and representation theory, we solve the functional equation
f1(xy) + f2(yx) + f3(xy-1) + f4(y-1x) = f5(x)f6(y)
on arbitrary compact groups, where all fi's are unknown square integrable functions. It turns out that the structure of its general solution is analogous to that of linear differential equations. Consequently, various special cases of the above equation, in particular, the Wilson equation and the d'Alembert long equation, are solved on compact groups.
DOI: 10.5802/jolt.638
Classification: 39B52, 22C05, 43A30, 22E45
Keywords: Functional equation, Fourier transform, representation theory 
@article{JOLT_2011_21_2_a7,
     author = {J. An and D. Yang},
     title = {Nonabelian {Harmonic} {Analysis} and {Functional} {Equations} on {Compact} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {427--456},
     year = {2011},
     volume = {21},
     number = {2},
     doi = {10.5802/jolt.638},
     zbl = {1219.39010},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.638/}
}
TY  - JOUR
AU  - J. An
AU  - D. Yang
TI  - Nonabelian Harmonic Analysis and Functional Equations on Compact Groups
JO  - Journal of Lie Theory
PY  - 2011
SP  - 427
EP  - 456
VL  - 21
IS  - 2
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.638/
DO  - 10.5802/jolt.638
ID  - JOLT_2011_21_2_a7
ER  - 
%0 Journal Article
%A J. An
%A D. Yang
%T Nonabelian Harmonic Analysis and Functional Equations on Compact Groups
%J Journal of Lie Theory
%D 2011
%P 427-456
%V 21
%N 2
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.638/
%R 10.5802/jolt.638
%F JOLT_2011_21_2_a7
J. An; D. Yang. Nonabelian Harmonic Analysis and Functional Equations on Compact Groups. Journal of Lie Theory, Volume 21 (2011) no. 2, pp. 427-456. doi: 10.5802/jolt.638

Cited by Sources: