AbstractWe relate the exponential integrability of the conjugate function $${\tilde{f}}$$
f
~
to the size of the gap in the essential range of f. Our main result complements a related theorem of Zygmund.
AbstractFollowing previous work in the continuous setup, we construct the unitarization of the horocyclic Radon transform on a homogeneous tree X and we show that it intertwines the quasi regular representations of the group of isometries of X on the tree itself and on the space of horocycles.
Conjugate Phase Retrieval in Paley–Wiener Space