Morera theorems via microlocal analysis

被引：2
|
作者：
Globevnik, J
Quinto, ET
机构：
[1] UNIV LJUBLJANA,DEPT MATH,LJUBLJANA,SLOVENIA
[2] TUFTS UNIV,DEPT MATH,MEDFORD,MA 02155
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 1996年 / 6卷 / 01期
关键词：
Morera theorem; Radon transform; support theorem; microlocal analysis; Fourier integral operators;
D O I：
10.1007/BF02921565
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove Morera theorems for curves in the plane using microlocal analysis. The key is that microlocal smoothness of functions is reflected by smoothness of their Morera integrals on curves-their Radon transforms. Parallel support theorems for the associated Radon transforms follow from our arguments by a simple correspondence.
引用
收藏
页码：19 / 30
页数：12
相关论文
共 46 条
  • [21] Microlocal Analysis of Generalized Pullbacks of Colombeau Functions
    Haller, Simon
    ACTA APPLICANDAE MATHEMATICAE, 2009, 105 (01) : 83 - 109
  • [22] Microlocal analysis and its application to SAR imaging
    Zhang, Guoping
    Liu, Fengshan
    Shi, Xiquan
    Xia, Shugao
    DISCRETE AND COMPUTATIONAL MATHEMATICS, 2008, : 331 - +
  • [23] Microlocal analysis for Gelfand-Shilov spaces
    Rodino, Luigi
    Wahlberg, Patrik
    ANNALI DI MATEMATICA PURA ED APPLICATA, 2023, 202 (05) : 2379 - 2420
  • [24] Microlocal Analysis of Generalized Pullbacks of Colombeau Functions
    Simon Haller
    Acta Applicandae Mathematicae, 2009, 105
  • [25] Microlocal analysis of synthetic aperture radar imaging
    Nolan, CJ
    Cheney, M
    JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2004, 10 (02) : 133 - 148
  • [26] Nonempty interior of configuration sets via microlocal partition optimization
    Allan Greenleaf
    Alex Iosevich
    Krystal Taylor
    Mathematische Zeitschrift, 2024, 306
  • [27] MICROLOCAL ANALYSIS OF DOPPLER SYNTHETIC APERTURE RADAR
    Felea, Raluca
    Gaburro, Romina
    Greenleaf, Allan
    Nolan, Clifford
    INVERSE PROBLEMS AND IMAGING, 2019, 13 (06) : 1283 - 1307
  • [28] Microlocal Analysis of the Doppler Transform on R3
    Karthik Ramaseshan
    Journal of Fourier Analysis and Applications, 2004, 10 : 73 - 82
  • [29] Microlocal Analysis of Generalized Radon Transforms from Scattering
    Webber, James W.
    Quinto, Eric Todd
    SIAM JOURNAL ON IMAGING SCIENCES, 2021, 14 (03) : 976 - 1003
  • [30] Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, II: Microlocal analysis
    Garetto, Claudia
    Jaeh, Christian
    Ruzhansky, Michael
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (10) : 7881 - 7905
12345