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7552481 
Journal Article 
ON QUANTITATIVE UNIQUE CONTINUATION PROPERTIES OF FRACTIONAL SCHRODINGER EQUATIONS: DOUBLING, VANISHING ORDER AND NODAL DOMAIN ESTIMATES 
Ruland, A 
2017 
Yes 
American Mathematical Society. Transactions
ISSN: 0002-9947 
AMER MATHEMATICAL SOC 
PROVIDENCE 
369 
4 
2311-2362 
WOS:000391381000003 
In this article we determine bounds on the maximal order of vanishing for eigenfunctions of a generalized Dirichlet-to-Neumann map (which is associated with fractional Schrodinger equations) on a compact, smooth Riemannian manifold, (M, g), without boundary. Moreover, with only slight modifications these results generalize to equations with C-1 potentials. Here Carleman estimates are a key tool. These yield a quantitative three balls inequality which implies quantitative bulk and boundary doubling estimates and hence leads to the control of the maximal order of vanishing. Using the boundary doubling property, we prove upper bounds on the Hn-1-measure of nodal domains of eigenfunctions of the generalized Dirichlet-to-Neumann map on analytic manifolds.