In this paper we establish the space-like strong unique continuation for nonlocal equations of type (∂t−Δ)su=Vu, 0<s<1. The proof our main result, Theorem 1.1, is achieved via a conditional elliptic doubling property solutions to appropriate extension problem, followed by blowup analysis.

We demonstrate, both analytically and experimentally, free-space pin-like optical vortex beams (POVBs).Such angular-momentum-carrying feature tunable peak intensity undergo robust anti-diffracting propagation, realized by judiciously modulating the amplitude phase profile of a standard laser beam. Specifically, they are generated superimposing radially-symmetric power-law on helical structure, ...