We consider the functional equation f(z+σ) - f(z) = g(z) where σ is a complex number, f and g are entire functions of a complex variable z, with growth conditions. We prove the existence of certain types of solutions of this equation by an a priori estimate method in certain weighted L2-spaces.
@article{urn:eudml:doc:41486,
title = {Sums of an entire function in certain weighted L2-spaces.},
journal = {Publicacions Matem\`atiques},
volume = {47},
year = {2003},
pages = {211-236},
zbl = {1038.30012},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41486}
}
Brive, Bruno. Sums of an entire function in certain weighted L2-spaces.. Publicacions Matemàtiques, Tome 47 (2003) pp. 211-236. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41486/