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Weak approximation of SDEs for tempered distributions and applications
Advances in Computational Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yuga Iguchi, Toshihiro Yamada
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AMALGAMS OF KUCERA TYPE AND TEMPERED DISTRIBUTIONS
Analysis, 1998The authors in this paper introduce a new class of amalgams of Kucera type and tempered distributions by defining the space \(L^k_{p,q}\) which reduces to the classical amalgams when \(k= 0\); and coincides with the space \(L^k_2\) when \(p= q=2\). Several topological properties, and investigation of the behaviour of a Fourier transform on such spaces ...
Betancor, Jorge J., González, Benito J.
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The support of tempered distributions
Mathematical Proceedings of the Cambridge Philosophical Society, 2008AbstractWe identify the support of a tempered distribution by evaluation of a sequence of test functions against the Fourier transform of the distribution. This improves previous results by removing the restriction that the distribution's Fourier transform be in $L^1_{loc}$ and be of polynomial growth.
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The Space of Tempered Distributions
2013The action of the Fourier transform is extended to the setting of tempered distributions and several distinguished subclasses of tempered distributions are introduced and studied, including homogeneous and principal value distributions. Significant applications to harmonic analysis and partial differential equations are singled out.
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Asian-European Journal of Mathematics, 2009
We define a new convolution ⊗ : 𝒮'(ℝ × ℝ+) × 𝒟(ℝ) → 𝒮'(ℝ × ℝ+) and derive the convolution theorems for wavelet transform and dual wavelet transform in the context of tempered distributions. By using the new convolution, we construct a Boehmian space containing the tempered distributions on ℝ × ℝ+.
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We define a new convolution ⊗ : 𝒮'(ℝ × ℝ+) × 𝒟(ℝ) → 𝒮'(ℝ × ℝ+) and derive the convolution theorems for wavelet transform and dual wavelet transform in the context of tempered distributions. By using the new convolution, we construct a Boehmian space containing the tempered distributions on ℝ × ℝ+.
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Laguerre-tempered distributions and their expansions
Acta Mathematica Hungarica, 1995Let \(u_\alpha= e^{- x} x^\alpha\) for \(0< x< \infty\) and let \((l^\alpha_n)\), \(n= 0, 1, 2,\dots\), be a sequence of polynomials, orthogonal on \((0, \infty)\) with respect to the weight \(u_\alpha\). There is considered the space \(\check Z^\alpha\) of functions \(f\in C^\infty(0, \infty)\) such that for every \(p\in \mathbb{R}\) and \(m\in ...
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Tempered Distributions and the Fourier Transform
1998In attempting to define the Fourier transform of a distribution t (x), we would like to use the formula (in R 1) $$ \hat t\left( u \right) = F\left( {t\left( x \right)} \right) = \int_{ - \infty }^\infty {e^{iux} t\left( x \right)dx.} $$ (1) .
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