Characterization of surjective convolution operators on Sato's hyperfunctions

Michael Langenbruch. "Characterization of surjective convolution operators on Sato's hyperfunctions." Banach Center Publications 88.1 (2010): 185-193. <http://eudml.org/doc/281860>.

@article{MichaelLangenbruch2010,
abstract = {Let $μ ∈ (ℝ^\{d\})^\{\prime \}$ be an analytic functional and let $T_μ$ be the corresponding convolution operator on Sato’s space $ (ℝ^\{d\})$ of hyperfunctions. We show that $T_μ$ is surjective iff $T_μ$ admits an elementary solution in $ (ℝ^\{d\})$ iff the Fourier transform μ̂ satisfies Kawai’s slowly decreasing condition (S). We also show that there are $0 ≠ μ ∈ (ℝ^\{d\})^\{\prime \}$ such that $T_μ$ is not surjective on $ (ℝ^\{d\})$.},
author = {Michael Langenbruch},
journal = {Banach Center Publications},
keywords = {hyperfunctions; convolution operators; surjectivity; analytic functionals},
language = {eng},
number = {1},
pages = {185-193},
title = {Characterization of surjective convolution operators on Sato's hyperfunctions},
url = {http://eudml.org/doc/281860},
volume = {88},
year = {2010},
}

TY - JOUR
AU - Michael Langenbruch
TI - Characterization of surjective convolution operators on Sato's hyperfunctions
JO - Banach Center Publications
PY - 2010
VL - 88
IS - 1
SP - 185
EP - 193
AB - Let $μ ∈ (ℝ^{d})^{\prime }$ be an analytic functional and let $T_μ$ be the corresponding convolution operator on Sato’s space $ (ℝ^{d})$ of hyperfunctions. We show that $T_μ$ is surjective iff $T_μ$ admits an elementary solution in $ (ℝ^{d})$ iff the Fourier transform μ̂ satisfies Kawai’s slowly decreasing condition (S). We also show that there are $0 ≠ μ ∈ (ℝ^{d})^{\prime }$ such that $T_μ$ is not surjective on $ (ℝ^{d})$.
LA - eng
KW - hyperfunctions; convolution operators; surjectivity; analytic functionals
UR - http://eudml.org/doc/281860
ER -