# Characterization of surjective convolution operators on Sato's hyperfunctions

Banach Center Publications (2010)

- Volume: 88, Issue: 1, page 185-193
- ISSN: 0137-6934

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topMichael 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 -