Distributional Mexican hat wavelet transform

被引：0
作者：
Abhishek Singh
机构：
[1] Banasthali Vidhyapith,Department of Mathematics and Statistics
来源：
The Journal of Analysis | 2020年 / 28卷
关键词：
Distribution space; Wavelet transform; Mexican hat wavelet; Weierstrass transform; Asymptotic behaviour; Primary 44A15; 42C15; Secondary 46F12;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Theory of Weierstrass transform is ventured to derive properties of the Mexican hat wavelet transform by Pathak and Singh (Integral Transforms and Special Function 27(6): 468–483, 2016). In this paper, distributional Mexican hat wavelet transform is studied and asymptotic behaviour for the same is discussed. Further, an inversion formula is established by interpreting convergence in the weak distributional sense.
引用
收藏
页码：533 / 544
页数：11
相关论文
共 50 条
  • [1] Distributional Mexican hat wavelet transform
    Singh, Abhishek
    JOURNAL OF ANALYSIS, 2020, 28 (02) : 533 - 544
  • [2] Mexican hat wavelet transform of distributions
    Pathak, R. S.
    Singh, Abhishek
    INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2016, 27 (06) : 468 - 483
  • [3] Representation theorems for the Mexican hat wavelet transform
    Singh, Abhishek
    Raghuthaman, Nikhila
    Rawat, Aparna
    Singh, Jagdev
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (07) : 3914 - 3924
  • [4] Mexican hat wavelet transform of generalized functions in G′ spaces
    Rawat, Aparna
    Singh, Abhishek
    PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2021, 131 (02):
  • [5] Three-dimensional profilometry based on mexican hat wavelet transform
    Zhou, Xiang
    Zhao, Hong
    Guangxue Xuebao/Acta Optica Sinica, 2009, 29 (01): : 197 - 202
  • [6] Distributional Wavelet Transform
    R. S. Pathak
    Abhishek Singh
    Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2016, 86 : 273 - 277
  • [7] Distributional Wavelet Transform
    Pathak, R. S.
    Singh, Abhishek
    PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES, 2016, 86 (02) : 273 - 277
  • [8] AN EXTENSION OF DISTRIBUTIONAL WAVELET TRANSFORM
    Roopkumar, R.
    COLLOQUIUM MATHEMATICUM, 2009, 115 (02) : 195 - 206
  • [9] A Family of Mexican Hat Wavelet Stieltjes Transform for Unbounded Non-decreasing Functions
    Rawat, Aparna
    Singh, Abhishek
    NATIONAL ACADEMY SCIENCE LETTERS-INDIA, 2024,
  • [10] Analysis of wave overtopping on a deck by 2D Mexican hat wavelet transform
    Kwon, SH
    Lee, HS
    Jung, DJ
    PROCEEDINGS OF THE FIFTH (2002) ISOPE PACIFIC/ASIA OFFSHORE MECHANICS SYMPOPSIUM, 2002, : 208 - 212
12345