Exponential bound of the integral of Hermite functions product with Gaussian weight

C. E. Wayne; V. Zharnitsky

doi:10.1016/j.jmaa.2022.126544

Exponential bound of the integral of Hermite functions product with Gaussian weight

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

Abstract

In this paper we derive a bound on the integral of a product of two Hermite-Gaussian functions with a Gaussian weight. We prove that such integrals decay exponentially in the difference of the indices of the Hermite-Gaussian functions. Such integrals arise naturally in mathematical physics and applied mathematics. The estimate is applied to a variational problem related to a Strichartz functional.

Original language	English (US)
Article number	126544
Journal	Journal of Mathematical Analysis and Applications
Volume	517
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2022.126544
State	Published - Jan 1 2023

Keywords

Exponential bound
Gaussian weight
Hermite functions
Strichartz functional

ASJC Scopus subject areas

Analysis
Applied Mathematics

Online availability

10.1016/j.jmaa.2022.126544

Library availability

Discover UIUC Full Text

Cite this

@article{38a0c49fe6ba4fb1a6d9a978eaf5009d,

title = "Exponential bound of the integral of Hermite functions product with Gaussian weight",

abstract = "In this paper we derive a bound on the integral of a product of two Hermite-Gaussian functions with a Gaussian weight. We prove that such integrals decay exponentially in the difference of the indices of the Hermite-Gaussian functions. Such integrals arise naturally in mathematical physics and applied mathematics. The estimate is applied to a variational problem related to a Strichartz functional.",

keywords = "Exponential bound, Gaussian weight, Hermite functions, Strichartz functional",

author = "Wayne, {C. E.} and V. Zharnitsky",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

year = "2023",

month = jan,

day = "1",

doi = "10.1016/j.jmaa.2022.126544",

language = "English (US)",

volume = "517",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Exponential bound of the integral of Hermite functions product with Gaussian weight

AU - Wayne, C. E.

AU - Zharnitsky, V.

PY - 2023/1/1

Y1 - 2023/1/1

N2 - In this paper we derive a bound on the integral of a product of two Hermite-Gaussian functions with a Gaussian weight. We prove that such integrals decay exponentially in the difference of the indices of the Hermite-Gaussian functions. Such integrals arise naturally in mathematical physics and applied mathematics. The estimate is applied to a variational problem related to a Strichartz functional.

AB - In this paper we derive a bound on the integral of a product of two Hermite-Gaussian functions with a Gaussian weight. We prove that such integrals decay exponentially in the difference of the indices of the Hermite-Gaussian functions. Such integrals arise naturally in mathematical physics and applied mathematics. The estimate is applied to a variational problem related to a Strichartz functional.

KW - Exponential bound

KW - Gaussian weight

KW - Hermite functions

KW - Strichartz functional

UR - http://www.scopus.com/inward/record.url?scp=85144087612&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85144087612&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2022.126544

DO - 10.1016/j.jmaa.2022.126544

M3 - Article

AN - SCOPUS:85144087612

SN - 0022-247X

VL - 517

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

M1 - 126544

ER -

Exponential bound of the integral of Hermite functions product with Gaussian weight

Abstract

Keywords

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this