William R. Green

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20122025

most citedDispersive Estimates for higher dimensional Schrödinger Operators with threshold eigenvalues I: The odd dimensional case

50 citations · 466 across the 27 of their papers we have counts for

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math.AP2012

Exponential Decay for dispersion managed solitons for general dispersion profiles

William R. Green, Dirk Hundertmark

We show that any weak solution of the Gabitov-Turitsyn equation describing dispersion managed solitons together with its Fourier transform decay exponentially. This strong regulari…

math.AP2012★ 4 cited

Dispersive estimates for matrix Schrödinger operators in dimension two

M. Burak Erdoğan, William R. Green

We consider the non-selfadjoint operator [\cH = [{array}{cc} -Δ+ μ-V_1 & -V_2 V_2 & Δ- μ+ V_1 {array}]] where $μ > 0$ and $V_{1}, V_{2}$ are real-valued decaying potentials. Such operator…

math.AP2012★ 30 cited

A weighted dispersive estimate for Schrödinger operators in dimension two

M. Burak Erdoğan, William R. Green

Let $H = - Δ + V$ , where $V$ is a real valued potential on $R^{2}$ satisfying $|V(x)|\les \la x\ra^{-3-}$. We prove that if zero is a regular point of the spectrum of $H = - Δ + V$ , then $$ \…

math.AP2012★ 31 cited

Dispersive estimates for Schrödinger operators in dimension two with obstructions at zero energy

M. Burak Erdogan, William R. Green

We investigate $L^{1} (R^{2}) \to L^{\infty} (R^{2})$ dispersive estimates for the Schrödinger operator $H = - Δ + V$ when there are obstructions, resonances or an eigenvalue, at zero energy. In…