HARMONIC ANALYSIS AND UNCERTAINTY PRINCIPLES FOR INTEGRAL TRANSFORMS GENERALIZING THE SPHERICAL MEAN OPERATOR

被引：0

作者：

Hleili, Khaled ^{[1
]}

Omri, Slim ^{[2
]}

Rachdi, Lakhdar Tannech ^{[3
]}

机构：

[1] Inst Appl Sci & Technol Tunis, Ctr Urbain Nord, Dept Math & Informat, BP 676, Tunis 1080, Tunisia

[2] Campus Univ, Preparatory Inst Engn Study, Nambeul 80000, Tunisia

[3] Fac Sci Tunis, Dept Math, Tunis, Tunisia

来源：

BULLETIN OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 4卷 / 01期

关键词：

Integral transform; Fourier transform; Inversion formula; Uncertainty principles;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For m,n is an element of N; m <= n >= 1, we define an integral transform R-m,R-n, that generalizes the spherical mean operator. We establish many harmonic analysis results for the Fourier transform p(m,n) connected with R-m,R-n. Next, we establish inversion formulas for the operator R-m,R-n and its dual (t) R-m,R-n. Finally, we prove some uncertainty principles related to the Fourier transform P-m,P-n

引用

页码：29 / 61

页数：33

共 26 条

[11] The uncertainty principle: A mathematical survey [J].

Folland, GB ;

Sitaram, A .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 1997, 3 (03) :207-238

[12]

Havin V., 2012, UNCERTAINTY PRINCIPL

[13] AN INVERSE METHOD FOR THE PROCESSING OF SYNTHETIC APERTURE RADAR DATA [J].

HELLSTEN, H ;

ANDERSSON, LE .

INVERSE PROBLEMS, 1987, 3 (01) :111-124

[14]

Herberthson M., 1986, D3043032 NAT DEF RES

[15]

Hleili K., 2011, CUBO, V13

[16]

Jelassi M., 2004, FRACT CALC APPL ANAL, V7, P379

[17]

Lebedev N.N., 1972, SPECIAL FUNCTIONS TH

[18]

Morgan G. W., 1934, J LOND MATH SOC, V9, P178

[19]

Msehli N., 2009, J INEQUAL PURE APPL, V10

[20] Ranges and inversion formulas for spherical mean operator and its dual [J].

Nessibi, MM ;

Rachdi, LT ;

Trimeche, K .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 196 (03) :861-884

← 1 2 3 →