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An extension of distributional wavelet transform

100%

Roopkumar R.

Colloquium Mathematicum

2009

tom 115

nr 2

195-206

We construct a new Boehmian space containing the space 𝓢̃'(ℝⁿ×ℝ₊) and define the extended wavelet transform 𝓦 of a new Boehmian as a tempered Boehmian. In analogy to the distributional wavelet transform, it is proved that the extended wavelet transform is linear, one-to-one, and continuous with respect to δ-convergence as well as Δ-convergence.

Operational calculus and Fourier transform on Boehmians

63%

Karunakaran V., Roopkumar R.

Colloquium Mathematicum

2005

tom 102

nr 1

21-32

We define various operations on the space of ultra Boehmians like multiplication with certain analytic functions which are Fourier transforms of compactly supported distributions, polynomials, and characters $(e^{ist}, s,t ∈ ℝ)$, translation, differentiation. We also prove that the Fourier transform on the space of ultra Boehmians has all the operational properties as in the classical theory.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Roopkumar R.

1 Karunakaran V.

1 2009

1 2005

Wyniki wyszukiwania

An extension of distributional wavelet transform

Operational calculus and Fourier transform on Boehmians