Spectral Calculus for Schrödinger Operators in One and Three Dimensions

Shijun Zheng

Spectral Calculus for Schrödinger Operators in One and Three Dimensions

Shijun Zheng

Mathematical Sciences

Research output: Contribution to conference › Presentation

Abstract

In this talk we consider Hormander type spectral multiplier problem for Schrödinger operator with a critical potential in one and three dimensions. It is shown that the multiplier operator is bounded on L^p, Besov spaces and Triebel-Lizorkin spaces under the same sharp condition. We then derive Strichartz estimates for the corresponding wave equations. Our work is partially motivated by the standing wave problem for the quintic wave equation in 3+1 spacetime dimensions.

Original language	American English
State	Published - Nov 6 2006
Event	Analysis and Partioal Differential Equations Seminar - Duration: Nov 6 2006 → …

Conference

Conference	Analysis and Partioal Differential Equations Seminar
Period	11/6/06 → …

Disciplines

Mathematics
Physical Sciences and Mathematics

Keywords

Schrodinger Operators
Spectral Calculus

Cite this

@conference{de6800065b0249888f1e9fcd21ee10a4,

title = "Spectral Calculus for Schr{\"o}dinger Operators in One and Three Dimensions",

abstract = "In this talk we consider Hormander type spectral multiplier problem for Schr{\"o}dinger operator with a critical potential in one and three dimensions. It is shown that the multiplier operator is bounded on Lp, Besov spaces and Triebel-Lizorkin spaces under the same sharp condition. We then derive Strichartz estimates for the corresponding wave equations. Our work is partially motivated by the standing wave problem for the quintic wave equation in 3+1 spacetime dimensions.",

keywords = "Schrodinger Operators, Spectral Calculus",

author = "Shijun Zheng",

year = "2006",

month = nov,

day = "6",

language = "American English",

note = "Analysis and Partioal Differential Equations Seminar ; Conference date: 06-11-2006",

}

TY - CONF

T1 - Spectral Calculus for Schrödinger Operators in One and Three Dimensions

AU - Zheng, Shijun

PY - 2006/11/6

Y1 - 2006/11/6

N2 - In this talk we consider Hormander type spectral multiplier problem for Schrödinger operator with a critical potential in one and three dimensions. It is shown that the multiplier operator is bounded on Lp, Besov spaces and Triebel-Lizorkin spaces under the same sharp condition. We then derive Strichartz estimates for the corresponding wave equations. Our work is partially motivated by the standing wave problem for the quintic wave equation in 3+1 spacetime dimensions.

AB - In this talk we consider Hormander type spectral multiplier problem for Schrödinger operator with a critical potential in one and three dimensions. It is shown that the multiplier operator is bounded on Lp, Besov spaces and Triebel-Lizorkin spaces under the same sharp condition. We then derive Strichartz estimates for the corresponding wave equations. Our work is partially motivated by the standing wave problem for the quintic wave equation in 3+1 spacetime dimensions.

KW - Schrodinger Operators

KW - Spectral Calculus

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpres/424

M3 - Presentation

T2 - Analysis and Partioal Differential Equations Seminar

Y2 - 6 November 2006

ER -

Spectral Calculus for Schrödinger Operators in One and Three Dimensions

Abstract

Conference

Disciplines

Keywords

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