Matthew D. Blair

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math.AP2024

$L^{p} - L^{q}$ resolvent restriction estimates for submanifolds

Matthew D. Blair, Chamsol Park

We consider restriction analogues on hypersurfaces of the uniform Sobolev inequalities in Kenig, Ruiz, and Sogge and the resolvent estimates in Dos Santos Ferreira, Kenig, and Salo…

math.AP2024

$L^{q}$ Estimates on the Restriction of Schrödinger Eigenfunctions with singular potentials

Matthew D. Blair, Chamsol Park

We consider eigenfunction estimates in $L^{p}$ for Schrödinger operators, $H_{V} = - Δ_{g} + V (x)$ , on compact Riemannian manifolds $(M, g)$ . Eigenfunction estimates over the full manifolds w…

math.AP2016

On logarithmic improvements of critical geodesic restriction bounds in the presence of nonpositive curvature

Matthew D. Blair

We consider upper bounds on the growth of $L^{p}$ norms of restrictions of eigenfunctions and quasimodes to geodesic segments in a nonpositively curved manifold in the high frequency…

Lp−Lq resolvent restriction estimates for submanifolds

Lq Estimates on the Restriction of Schrödinger Eigenfunctions with singular potentials

On logarithmic improvements of critical geodesic restriction bounds in the presence of nonpositive curvature

$L^{p} - L^{q}$ resolvent restriction estimates for submanifolds

$L^{q}$ Estimates on the Restriction of Schrödinger Eigenfunctions with singular potentials