RT Journal Article
T1 The Fourier extension operator of distributions in Sobolev spaces of the sphere and the Helmholtz equation
A1 Barceló, Juan Antonio
A1 Folch Gabayet, Magali
A1 Luque Martínez, Teresa Elvira
A1 Pérez Esteva, Salvador
A1 Vilela, María de la Cruz
AB The purpose of this paper is to characterize the entire solutions of the homogeneous Helmholtz equation (solutions in ℝd) arising from the Fourier extension operator of distributions in Sobolev spaces of the sphere  with α ∈ ℝ. We present two characterizations. The first one is written in terms of certain L2-weighted norms involving real powers of the spherical Laplacian. The second one is in the spirit of the classical description of the Herglotz wave functions given by P. Hartman and C. Wilcox. For α > 0 this characterization involves a multivariable square function evaluated in a vector of entire solutions of the Helmholtz equation, while for α < 0 it is written in terms of an spherical integral operator acting as a fractional integration operator. Finally, we also characterize all the solutions that are the Fourier extension operator of distributions in the sphere.
PB Cambridge University Press
SN 0308-2105
YR 2020
FD 2020
LK https://hdl.handle.net/20.500.14352/99754
UL https://hdl.handle.net/20.500.14352/99754
LA eng
NO Barceló JA, Folch-Gabayet M, Luque T, Pérez-Esteva S, Vilela MC. 2021 The Fourier extension operator of distributions in Sobolev spaces of the sphere and the Helmholtz equation. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 151, 1768–1789. (doi:10.1017/prm.2020.80)
DS Docta Complutense
RD 6 abr 2025