Волчков Вит. В.

Zero sets of solutions of the hyperbolic Darboux equation

Page: 
7

Zero sets of solutions of the hyperbolic Darboux equation Volchkov V. V. and Volchkov Vit. V.
A hyperbolic analog of the generalized Darboux equation is considered. We investigate the structure of zero sets of its solutions for the case where the solution is a radial function of second variable. We show that every solution vanishing on some annulus must be zero in some other annulus containing the first one.

Keywords: Darboux equation, hyperbolic plane, zero sets, uniqueness theorems, transmutation maps.