M. Erdoğan

activity

20122025

most citedDispersive estimates for four dimensional Schrödinger and wave equations with obstructions at zero energy

45 citations · 163 across the 14 of their papers we have counts for

collaborators

14 papers

math.AP2025

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

M. Burak Erdogan, Michael Goldberg, William Green

We consider fractional Schrödinger operators $H = (- Δ)^{α} + V (x)$ in $n$ dimensions with real-valued potential $V$ when $n > 2 α$ , $α > 1$ . We show that the wave operators extend to bounded…

math.AP2025

Dispersive estimates for fractional order Schrödinger operators

M. Burak Erdogan, Michael Goldberg, William Green

We prove dispersive bounds for fractional Schrödinger operators on $R^{n}$ of the form $H = (- Δ)^{α} + V$ with $V$ a real-valued, decaying potential and $α \in / N$ . We deri…

math.AP2025

$L^{p}$ boundedness of wave operators for higher order schrödinger operators with threshold eigenvalues

M. Burak Erdogan, William R. Green, Kevin LaMaster

We consider the higher order Schrödinger operator $H = (- Δ)^{m} + V (x)$ in $n$ dimensions with real-valued potential $V$ when $n > 2 m$ , $m \in N$ when $H$ has a threshold eigenvalue…

math.AP2024★ 3 cited

$L^{p}$ -continuity of wave operators for higher order Schrödinger operators with threshold eigenvalues in high dimensions

M. Burak Erdogan, William R. Green, Kevin LaMaster

We consider the higher order Schrödinger operator $H = (- Δ)^{m} + V (x)$ in $n$ dimensions with real-valued potential $V$ when $n > 4 m$ , $m \in N$ . We adapt our recent results for $m…

math.AP2022★ 12 cited

A note on endpoint $L^{p}$ -continuity of wave operators for classical and higher order Schrödinger operators

M. Burak Erdogan, William R. Green

We consider the higher order Schrödinger operator $H = (- Δ)^{m} + V (x)$ in $n$ dimensions with real-valued potential $V$ when $n > 2 m$ , $m \in N$ . We adapt our recent results for $m…

math.AP2020★ 12 cited

On the one dimensional Dirac equation with potential

Burak Erdogan, William R. Green

We investigate $L^{1} \to L^{\infty}$ dispersive estimates for the one dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies the natural…

math.AP2018★ 2 cited

The Massless Dirac Equation in Two Dimensions: Zero-Energy Obstructions and Dispersive Estimates

Burak Erdogan, Michael Goldberg, William R. Green

We investigate $L^{1} \to L^{\infty}$ dispersive estimates for the massless two dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies th…

math.AP2017★ 13 cited

Dispersive estimates for massive Dirac operators in dimension two

M. Burak Erdoğan, William R. Green, Ebru Toprak

We study the massive two dimensional Dirac operator with an electric potential. In particular, we show that the $t^{- 1}$ decay rate holds in the $L^{1} \to L^{\infty}$ setting if the th…

math.AP2017★ 17 cited

Limiting absorption principle and Strichartz estimates for Dirac operators in two and higher dimensions

Burak Erdogan, Michael Goldberg, William R. Green

In this paper we consider Dirac operators in $R^{n}$ , $n \geq 2$ , with a potential $V$ . Under mild decay and continuity assumptions on $V$ and some spectral assumptions on the…

math.AP2017★ 17 cited

On the $L^{p}$ boundedness of wave operators for two-dimensional Schrödinger operators with threshold obstructions

Burak Erdogan, Michael Goldberg, William R. Green

Let $H = - Δ + V$ be a Schrödinger operator on $L^{2} (R^{2})$ with real-valued potential $V$ , and let $H_{0} = - Δ$ . If $V$ has sufficient pointwise decay, the wave operators $W_{\pm}=s-…

math.AP2016★ 21 cited

Dispersive estimates for Dirac Operators in dimension three with obstructions at threshold energies

Burak Erdogan, William R. Green, Ebru Toprak

We investigate $L^{1} \to L^{\infty}$ dispersive estimates for the three dimensional Dirac equation with a potential. We also classify the structure of obstructions at the thresholds of…

math.AP2016★ 17 cited

The Dirac equation in two dimensions: Dispersive estimates and classification of threshold obstructions

M. Burak Erdogan, William R. Green

We investigate dispersive estimates for the two dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies a $t^{- 1}$ decay rate as an o…

math.AP2013★ 45 cited

Dispersive estimates for four dimensional Schrödinger and wave equations with obstructions at zero energy

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

We investigate $L^{1} (R^{4}) \to L^{\infty} (R^{4})$ dispersive estimates for the Schrödinger operator $H = - Δ + V$ when there are obstructions, a resonance or an eigenvalue, at…

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…

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

Dispersive estimates for fractional order Schrödinger operators

Lp boundedness of wave operators for higher order schrödinger operators with threshold eigenvalues

Lp-continuity of wave operators for higher order Schrödinger operators with threshold eigenvalues in high dimensions

A note on endpoint Lp-continuity of wave operators for classical and higher order Schrödinger operators

On the one dimensional Dirac equation with potential

The Massless Dirac Equation in Two Dimensions: Zero-Energy Obstructions and Dispersive Estimates

Dispersive estimates for massive Dirac operators in dimension two

Limiting absorption principle and Strichartz estimates for Dirac operators in two and higher dimensions

On the Lp boundedness of wave operators for two-dimensional Schrödinger operators with threshold obstructions

Dispersive estimates for Dirac Operators in dimension three with obstructions at threshold energies

The Dirac equation in two dimensions: Dispersive estimates and classification of threshold obstructions

Dispersive estimates for four dimensional Schrödinger and wave equations with obstructions at zero energy

Dispersive estimates for matrix Schrödinger operators in dimension two

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

$L^{p}$ boundedness of wave operators for higher order schrödinger operators with threshold eigenvalues

$L^{p}$ -continuity of wave operators for higher order Schrödinger operators with threshold eigenvalues in high dimensions

A note on endpoint $L^{p}$ -continuity of wave operators for classical and higher order Schrödinger operators

On the $L^{p}$ boundedness of wave operators for two-dimensional Schrödinger operators with threshold obstructions