Convolution in $(W^p_{M, \ a})^{\prime }$-space

R. S. Pathak; S. K. Upadhyay

Displaying similar documents to “Convolution in ${(W_{M, a}^{p})}^{'}$ -space”

Beurling-Gevrey tempered ultradistributions as boundary values

Pilipovic, Stevan (1991)

Portugaliae mathematica

Similarity:

On the representation of trajectories of bilinear systems and its applications

Sergej Čelikovský (1987)

Kybernetika

Similarity:

Maximal estimates for nonsymmetric semigroups

Jacek Zienkiewicz (1994)

Studia Mathematica

Similarity:

Exponentially convex functions on a cone in a Lie group

S. Lachterman (1966)

Studia Mathematica

Similarity:

Characteristic Cauchy problems and solutions of formal power series

Sunao Ouchi (1983)

Annales de l'institut Fourier

Similarity:

Let $L (z, \partial_{z}) = (\partial_{z_{0}})^{k} - A (z, \partial_{z})$ be a linear partial differential operator with holomorphic coefficients, where $A (z, \partial_{z}) = \sum_{j = 0}^{k - 1} A_{j} (z, \partial_{z^{'}}) (\partial_{z_{0}})^{j}, ord . A (z, \partial_{z}) = m > k$ and $z = (z_{0}, z^{'}) \in C^{n + 1} .$ We consider Cauchy problem with holomorphic data $L (z, \partial_{z}) u (z) = f (z), (\partial_{z_{0}})^{i} u (0, z^{'}) = {\hat{u}}_{i} (z^{'}) (0 \leq i \leq k - 1) .$ We can easily get a formal solution $\hat{u} (z) = \sum_{n = 0}^{\infty} {\hat{u}}_{n} (z^{'}) (z_{0})^{n} / n!$ , bu in general it diverges. We show under some conditions that for any sector $S$ with the opening less that a constant determined by $L (z, \partial_{z})$ , there is a function $u_{S} (z)$ holomorphic except on ${z_{0} = 0}$ such that $L (z, \partial_{z}) u_{S} (z) = f (z)$ and $u_{S} (z) \sim \hat{u} (z)$ as $z_{0} \to 0$ in $S$ .

On the theorem of Ivasev-Musatov. I

Thomas-William Korner (1977)

Annales de l'institut Fourier

Similarity:

We give a new version of Ivasev-Musatov’s construction of a measure whose support has Lebesgue measure zero but whose Fourier transform drops away extremely rapidly.

Integration of the first order partial differential inequality with distributions

W. Mlak (1963)

Colloquium Mathematicae

Similarity:

Displaying similar documents to “Convolution in ( W M , a p ) ' -space”

Beurling-Gevrey tempered ultradistributions as boundary values

On the representation of trajectories of bilinear systems and its applications

Maximal estimates for nonsymmetric semigroups

Exponentially convex functions on a cone in a Lie group

Characteristic Cauchy problems and solutions of formal power series

On the theorem of Ivasev-Musatov. I

Integration of the first order partial differential inequality with distributions

Displaying similar documents to “Convolution in ${(W_{M, a}^{p})}^{'}$ -space”