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Taylor formula for distributions [Book]

Bogdan Ziemian (1988)

Taylor-type expansion of the $k$ -th derivative of the Dirac delta in $u (x_{1}, \dots, x_{n}) - t$ .

Aguirre, Manuel A. (2002)

Novi Sad Journal of Mathematics

Tempered nontangential boundedness

B. Marshall (1980)

Studia Mathematica

The algebra of polynomials on the space of ultradifferentiable functions

Katarzyna Grasela (2010)

Banach Center Publications

We consider the space $^{ℳ}$ of ultradifferentiable functions with compact supports and the space of polynomials on $^{ℳ}$ . A description of the space $(^{ℳ})$ of polynomial ultradistributions as a locally convex direct sum is given.

The distributional multiplicative product P ...

Manuel Aguirre Téllez, Susana Trione (1993)

Revista colombiana de matematicas

The divergent distribution product Xλ+Xμ-.

B. Fisher (1976)

Collectanea Mathematica

The domain of attraction of a normal distribution in a Hilbert space

M. Kłosowska (1972)

Studia Mathematica

The Fourier transform of distributions and the exchange formula

B. Fisher, Li Chen Kuan, A. Takači (1988)

Matematički Vesnik

The Kontorovich-Lebedev Transformation of Distributions.

Ram S. Pathak, Jagdish N. Pandey (1979)

Mathematische Zeitschrift

The linear Cauchy problem for a class of differential equations with distributional coefficients.

Sarrico, C.O.R. (1995)

Portugaliae Mathematica

The multiplication functions of Kučera

Kelly McKennon (1979)

Czechoslovak Mathematical Journal

The neutrix convolution product in $Z^{'} (m)$ and the exchange formula.

Li, C.K., Koh, E.L. (1998)

International Journal of Mathematics and Mathematical Sciences

The Neutrix Convolution Product x -r,- ○ x μ,+

Brian Fisher, Emin Özcag (1991)

Publications de l'Institut Mathématique

The neutrix product of the distributions $x_{+}^{λ} ln x_{+}$ and $x_{-}^{- λ - r}$ .

Fisher, Brian, Al-Sirehy, Fatma (1999)

Bulletin of the Malaysian Mathematical Society. Second Series

The prime number theorem for Beurling's generalized numbers. New cases

Jan-Christoph Schlage-Puchta, Jasson Vindas (2012)

Acta Arithmetica

The product of a function and a Boehmian

Dennis Nemzer (1993)

Colloquium Mathematicae

Let A be the class of all real-analytic functions and β the class of all Boehmians. We show that there is no continuous operation on β which is ordinary multiplication when restricted to A.

The product of distributions on $R^{m}$

Cheng Lin-Zhi, Brian Fisher (1992)

Commentationes Mathematicae Universitatis Carolinae

The fixed infinitely differentiable function $ρ (x)$ is such that ${n ρ (n x)}$ is a regular sequence converging to the Dirac delta function $δ$ . The function $δ_{𝐧} (𝐱)$ , with $𝐱 = (x_{1}, \dots, x_{m})$ is defined by $δ_{𝐧} (𝐱) = n_{1} ρ (n_{1} x_{1}) \dots n_{m} ρ (n_{m} x_{m}) .$ The product $f \circ g$ of two distributions $f$ and $g$ in $𝒟_{m}^{'}$ is the distribution $h$ defined by $\underset{n_{1} \to \infty}{error} \dots \underset{n_{m} \to \infty}{error} 〈 f_{𝐧} g_{𝐧}, φ 〉 = 〈 h, φ 〉,$ provided this neutrix limit exists for all $φ (𝐱) = φ_{1} (x_{1}) \dots φ_{m} (x_{m})$ , where $f_{𝐧} = f * δ_{𝐧}$ and $g_{𝐧} = g * δ_{𝐧}$ .

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