The Continuous Fractional Wavelet Transform on W-Type Spaces

Q4 Mathematics

Journal of the Indian Mathematical Society Pub Date : 2018-06-01 DOI:10.18311/JIMS/2018/20984

Anuj Kumar, S. Upadhyay

引用次数: 0

Abstract

An n-dimensional continuous fractional wavelet transform involving n-dimensional fractional Fourier transform is studied and its properties are obtained on Gel'fand and Shilov spaces of type W_M(Rⁿ), W^Ω (Cⁿ) and W^Ω_M (Cⁿ). It is shown that continuous fractional wavelet transform, W^α_ψΦ : W_M(Rⁿ) → W_M(Rⁿ × R₊), W^α_ψΦ : W^Ω (Cⁿ) → W^Ω (Cⁿ × R₊) and W^α_ψΦ : W^Ω_M (Cⁿ) → W^Ω_M (Cⁿ × R₊) are linear and continuous maps, where Rⁿ and Cⁿ are the usual Euclidean spaces.

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w型空间上的连续分数小波变换

研究了一种涉及n维分数阶傅里叶变换的n维连续分数阶小波变换，并在WM(Rn)、WΩ (Cn)和WΩM (Cn)型Gel'fand和Shilov空间上得到了它的性质。结果表明，连续分数小波变换WαψΦ: WM(Rn)→WM(Rn × R+)、WαψΦ: WΩ (Cn)→WΩ (Cn × R+)和WαψΦ: WΩM (Cn)→WΩM (Cn × R+)是线性连续映射，其中Rn和Cn是通常的欧几里得空间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of the Indian Mathematical Society Mathematics-Mathematics (all)

CiteScore

0.50

自引率

0.00%

发文量

期刊介绍： The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title ''the Journal of Indian Mathematical Society. The four issues of the Journal constitute a single volume and it is published in two parts: issues 1 and 2 (January to June) as one part and issues 3 and 4 (July to December) as the second part. The four issues of the Mathematics Student (another periodical of the Society) are published as a single yearly volume. Only the original research papers of high quality are published in the Journal of Indian Mathematical Society.