Abstract theory of pointwise decay with applications to wave and Schrödinger equations

Georgescu, Vladimir; Larenas, Manuel; Soffer, Avy

doi:10.48550/arxiv.1411.5763

Search citation statements

Order By: Relevance

Paper Sections

Select...

The Klein-gordon Equation With a Potential1

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2015

Publication Types

Select...

Other1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recalling (15), we need separate analysis for the contribution of the finite Born series, (16), and the singular portion of the expansion which is sensitive to the existence of zeroenergy resonances and eigenvalues, (17).…”

Section: The Klein-gordon Equation With a Potentialmentioning

confidence: 99%

See 1 more Smart Citation

Decay estimates for four dimensional Schrödinger, Klein-Gordon and wave equations with obstructions at zero energy

Green¹,

Toprak²

2015

Preprint

View full text Add to dashboard Cite

We investigate dispersive estimates for the Schrödinger operator H = −∆+V with V is a real-valued decaying potential when there are zero energy resonances and eigenvalues in four spatial dimensions. If there is a zero energy obstruction, we establish the low-energy expansionHere A0, A1 :while A2, A3 are operators between logarithmically weighted spaces, with A0, A1, A2 finite rank operators, further the operators are independent of time. We show that similar expansions are valid for the solution operators to Klein-Gordon and wave equations. Finally, we show that under certain orthogonality conditions, if there is a zero energy eigenvalue one can recover the |t| −2 bound as an operator from L 1 → L ∞ . Hence, recovering the same dispersive bound as the free evolution in spite of the zero energy eigenvalue.

show abstract

Section: The Klein-gordon Equation With a Potentialmentioning

confidence: 99%

“…L ∞ bounds on solutions to the wave equation has been studied, [4,3,9,11,6,26]. The dispersive nature of the Klein-Gordon has been studied in various senses [35,33,17]. The effect of threshold eigenvalues and resonances for wave-like equations has been studied in dimensions n ≤ 4, see [34,25,14].…”

Section: Introductionmentioning

confidence: 99%

Decay estimates for four dimensional Schrödinger, Klein-Gordon and wave equations with obstructions at zero energy

Green¹,

Toprak²

2015

Preprint

View full text Add to dashboard Cite

show abstract

Abstract theory of pointwise decay with applications to wave and Schrödinger equations

Cited by 1 publication

References 0 publications

Decay estimates for four dimensional Schrödinger, Klein-Gordon and wave equations with obstructions at zero energy

Decay estimates for four dimensional Schrödinger, Klein-Gordon and wave equations with obstructions at zero energy

Contact Info

Product

Resources

About