M. Erdogan

activity

20052026

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

31 citations · 119 across the 15 of their papers we have counts for

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14 papers · 1 filter

math.AP2026

Dispersive Estimates for Dirac Operators with General Domain Walls: One and Two Dimensions

M. Burak Erdogan, Joseph Kraisler, Amir Sagiv

We establish dispersive decay estimates for two-dimensional Dirac equations with bounded and unbounded domain walls, together with estimates for the analogous one-dimensional probl…

math.AP2023★ 2 cited

Dispersive estimates for higher order Schrödinger operators with scaling-critical potentials

M. Burak Erdogan, Michael Goldberg, William R. Green

We prove a family of dispersive estimates for the higher order Schrödinger equation $i u_{t} = (- Δ)^{m} u + V u$ for $m \in N$ with $m > 1$ and $2 m < n < 4 m$ . Here $V$ is a real-valued pote…

math.AP2023

Talbot Effect on the Sphere and Torus for $d \geq 2$

M. Burak Erdogan, Chi N. Y. Huynh, Ryan McConnell

We utilize exponential sum techniques to obtain upper and lower bounds for the fractal dimension of the graph of solutions to the linear Schrödinger equation on $S^{d}$ and…

math.AP2022★ 11 cited

Counterexamples to $L^{p}$ boundedness of wave operators for classical and higher order Schrödinger operators

M. Burak Erdogan, Michael Goldberg, William R. Green

We consider the higher order Schrödinger operator $H = (- Δ)^{m} + V (x)$ in $n$ dimensions with real-valued potential $V$ when $n > 4 m - 1$ , $m \in N$ . We show that for any $\frac{2n}{…

math.AP2021★ 19 cited

The $L^{p}$ -continuity of wave operators for higher order Schrödinger operators

M. Burak Erdogan, William Green

We consider the higher order Schrödinger operator $H = (- Δ)^{m} + V (x)$ in $n$ dimensions with real-valued potential $V$ when $n > 2 m$ , $m \in N$ , $m > 1$ . When $n$ is odd, we prove t…

math.AP2019

Strichartz Estimates for the Schrödinger Equation with a Measure-Valued Potential

M. Burak Erdogan, Michael Goldberg, William R. Green

We prove Strichartz estimates for the Schrödinger equation in $R^{n}$ , $n \geq 3$ , with a Hamiltonian $H = - Δ + μ$ . The perturbation $μ$ is a compactly supported measure in $\m…

Dispersive Estimates for Dirac Operators with General Domain Walls: One and Two Dimensions

Dispersive estimates for higher order Schrödinger operators with scaling-critical potentials

Talbot Effect on the Sphere and Torus for d≥2

Counterexamples to Lp boundedness of wave operators for classical and higher order Schrödinger operators

The Lp-continuity of wave operators for higher order Schrödinger operators

Strichartz Estimates for the Schrödinger Equation with a Measure-Valued Potential

Talbot Effect on the Sphere and Torus for $d \geq 2$

Counterexamples to $L^{p}$ boundedness of wave operators for classical and higher order Schrödinger operators

The $L^{p}$ -continuity of wave operators for higher order Schrödinger operators