On Hardy's theorem on SU(1, 1)

Takeshi Kawazoe; Jianming Liu

doi:10.1007/s11401-005-0557-2

On Hardy's theorem on SU(1, 1)

Takeshi Kawazoe, Jianming Liu

Faculty of Policy Management

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

1 Citation (Scopus)

Abstract

The classical Hardy theorem asserts that f and its Fourier transform f̂ can not both be very rapidly decreasing. This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform. However, on SU(1, 1) there are infinitely many "good" functions in the sense that f and its spherical Fourier transform f̂ both have good decay. In this paper, we shall characterize such functions on SU(1, 1).

Original language	English
Pages (from-to)	429-440
Number of pages	12
Journal	Chinese Annals of Mathematics. Series B
Volume	28
Issue number	4
DOIs	https://doi.org/10.1007/s11401-005-0557-2
Publication status	Published - 2007 Aug

Keywords

Heat kernel
Jacobi transform
Plancherel formula

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1007/s11401-005-0557-2

Cite this

@article{eb294870473545688207f393c70d9438,

title = "On Hardy's theorem on SU(1, 1)",

abstract = "The classical Hardy theorem asserts that f and its Fourier transform {\^f} can not both be very rapidly decreasing. This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform. However, on SU(1, 1) there are infinitely many {"}good{"} functions in the sense that f and its spherical Fourier transform {\^f} both have good decay. In this paper, we shall characterize such functions on SU(1, 1).",

keywords = "Heat kernel, Jacobi transform, Plancherel formula",

author = "Takeshi Kawazoe and Jianming Liu",

note = "Funding Information: Manuscript received September 5, 2005. Revised March 8, 2006. Published online July 2, 2007. ∗Department of Mathematics, Keio University at Fujisawa, Endo, Fujisawa, Kanagawa, 252-8520, Japan. E-mail: kawazoe@sfc.keio.ac.jp ∗∗Laboratory of Mathematics and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China. E-mail: liujm@math.pku.edu.cn ∗∗∗Project supported by Grant-in-Aid for Scientific Research (C) of Japan (No. 16540168) and the National Natural Science Foundation of China (No. 10371004).",

year = "2007",

month = aug,

doi = "10.1007/s11401-005-0557-2",

language = "English",

volume = "28",

pages = "429--440",

journal = "Chinese Annals of Mathematics. Series B",

issn = "0252-9599",

publisher = "Springer Verlag",

number = "4",

}

TY - JOUR

T1 - On Hardy's theorem on SU(1, 1)

AU - Kawazoe, Takeshi

AU - Liu, Jianming

N1 - Funding Information: Manuscript received September 5, 2005. Revised March 8, 2006. Published online July 2, 2007. ∗Department of Mathematics, Keio University at Fujisawa, Endo, Fujisawa, Kanagawa, 252-8520, Japan. E-mail: kawazoe@sfc.keio.ac.jp ∗∗Laboratory of Mathematics and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China. E-mail: liujm@math.pku.edu.cn ∗∗∗Project supported by Grant-in-Aid for Scientific Research (C) of Japan (No. 16540168) and the National Natural Science Foundation of China (No. 10371004).

PY - 2007/8

Y1 - 2007/8

N2 - The classical Hardy theorem asserts that f and its Fourier transform f̂ can not both be very rapidly decreasing. This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform. However, on SU(1, 1) there are infinitely many "good" functions in the sense that f and its spherical Fourier transform f̂ both have good decay. In this paper, we shall characterize such functions on SU(1, 1).

AB - The classical Hardy theorem asserts that f and its Fourier transform f̂ can not both be very rapidly decreasing. This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform. However, on SU(1, 1) there are infinitely many "good" functions in the sense that f and its spherical Fourier transform f̂ both have good decay. In this paper, we shall characterize such functions on SU(1, 1).

KW - Heat kernel

KW - Jacobi transform

KW - Plancherel formula

UR - http://www.scopus.com/inward/record.url?scp=34548097030&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548097030&partnerID=8YFLogxK

U2 - 10.1007/s11401-005-0557-2

DO - 10.1007/s11401-005-0557-2

M3 - Article

AN - SCOPUS:34548097030

SN - 0252-9599

VL - 28

SP - 429

EP - 440

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 4

ER -

On Hardy's theorem on SU(1, 1)

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this