Strichartz estimates for Schrödinger-Laguerre operators

Salem Ben Saïd

doi:10.1007/s00233-014-9617-9

Strichartz estimates for Schrödinger-Laguerre operators

Salem Ben Saïd

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

Abstract

In ×ⁿ× we consider the Schrödinger equation (formula presented.)with given boundary value on .öⁿ Here L_k = ||x||∆||_k−||x| is a differential-difference-multiplication operator on ×ⁿ where k is a multiplicity function for the Dunkl Laplacian Δk ≡0 In the case, L⁰ is the classical multi-dimensional Laguerre operator. In this paper we obtain Strichartz estimates for the Schrödinger equation (E¹). We then prove that Strichartz estimates for the Schrödinger equation (formula presented.)can be obtained from those for (E¹). The k≡0 case is already new.

Original language	English
Pages (from-to)	251-269
Number of pages	19
Journal	Semigroup Forum
Volume	90
Issue number	1
DOIs	https://doi.org/10.1007/s00233-014-9617-9
Publication status	Published - Feb 2014
Externally published	Yes

Keywords

Dunkl Laplacian
Holomorphic semigroups
Schrödinger equations
Strichartz estimates

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/s00233-014-9617-9

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title = "Strichartz estimates for Schr{\"o}dinger-Laguerre operators",

abstract = "In ×n× we consider the Schr{\"o}dinger equation (formula presented.)with given boundary value on .{\"o}n Here Lk = ||x||∆||k−||x| is a differential-difference-multiplication operator on ×n where k is a multiplicity function for the Dunkl Laplacian Δk ≡0 In the case, L0 is the classical multi-dimensional Laguerre operator. In this paper we obtain Strichartz estimates for the Schr{\"o}dinger equation (E1). We then prove that Strichartz estimates for the Schr{\"o}dinger equation (formula presented.)can be obtained from those for (E1). The k≡0 case is already new.",

keywords = "Dunkl Laplacian, Holomorphic semigroups, Schr{\"o}dinger equations, Strichartz estimates",

author = "{Ben Sa{\"i}d}, Salem",

note = "Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media New York.",

year = "2014",

month = feb,

doi = "10.1007/s00233-014-9617-9",

language = "English",

volume = "90",

pages = "251--269",

journal = "Semigroup Forum",

issn = "0037-1912",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Strichartz estimates for Schrödinger-Laguerre operators

AU - Ben Saïd, Salem

PY - 2014/2

Y1 - 2014/2

N2 - In ×n× we consider the Schrödinger equation (formula presented.)with given boundary value on .ön Here Lk = ||x||∆||k−||x| is a differential-difference-multiplication operator on ×n where k is a multiplicity function for the Dunkl Laplacian Δk ≡0 In the case, L0 is the classical multi-dimensional Laguerre operator. In this paper we obtain Strichartz estimates for the Schrödinger equation (E1). We then prove that Strichartz estimates for the Schrödinger equation (formula presented.)can be obtained from those for (E1). The k≡0 case is already new.

AB - In ×n× we consider the Schrödinger equation (formula presented.)with given boundary value on .ön Here Lk = ||x||∆||k−||x| is a differential-difference-multiplication operator on ×n where k is a multiplicity function for the Dunkl Laplacian Δk ≡0 In the case, L0 is the classical multi-dimensional Laguerre operator. In this paper we obtain Strichartz estimates for the Schrödinger equation (E1). We then prove that Strichartz estimates for the Schrödinger equation (formula presented.)can be obtained from those for (E1). The k≡0 case is already new.

KW - Dunkl Laplacian

KW - Holomorphic semigroups

KW - Schrödinger equations

KW - Strichartz estimates

UR - http://www.scopus.com/inward/record.url?scp=84939877994&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84939877994&partnerID=8YFLogxK

U2 - 10.1007/s00233-014-9617-9

DO - 10.1007/s00233-014-9617-9

M3 - Article

AN - SCOPUS:84939877994

SN - 0037-1912

VL - 90

SP - 251

EP - 269

JO - Semigroup Forum

JF - Semigroup Forum

IS - 1

ER -

Strichartz estimates for Schrödinger-Laguerre operators

Abstract

Keywords

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