One-parameter semigroups in the convolution algebra of rapidly decreasing distributions

"One-parameter semigroups in the convolution algebra of rapidly decreasing distributions." Colloquium Mathematicae 128.1 (2012): 49-68. <http://eudml.org/doc/283529>.

@article{Unknown2012,
abstract = {The paper is devoted to infinitely differentiable one-parameter convolution semigroups in the convolution algebra $^\{\prime \}_\{C\}(ℝⁿ;M_\{m×m\})$ of matrix valued rapidly decreasing distributions on ℝⁿ. It is proved that $G ∈ ^\{\prime \}_\{C\}(ℝⁿ;M_\{m×m\})$ is the generating distribution of an i.d.c.s. if and only if the operator $∂_\{t\} ⊗ _\{m×m\} - G∗ $ on $ℝ^\{1+n\}$ satisfies the Petrovskiĭ condition for forward evolution. Some consequences are discussed.},
journal = {Colloquium Mathematicae},
keywords = {one-parameter convolution semigroup of rapidly decreasing distributions; partial differential operator with constant coefficients; Cauchy problem; fundamental solution with support in a halfspace; Petrovskiĭ condition; slowly increasing function},
language = {eng},
number = {1},
pages = {49-68},
title = {One-parameter semigroups in the convolution algebra of rapidly decreasing distributions},
url = {http://eudml.org/doc/283529},
volume = {128},
year = {2012},
}

TY - JOUR
TI - One-parameter semigroups in the convolution algebra of rapidly decreasing distributions
JO - Colloquium Mathematicae
PY - 2012
VL - 128
IS - 1
SP - 49
EP - 68
AB - The paper is devoted to infinitely differentiable one-parameter convolution semigroups in the convolution algebra $^{\prime }_{C}(ℝⁿ;M_{m×m})$ of matrix valued rapidly decreasing distributions on ℝⁿ. It is proved that $G ∈ ^{\prime }_{C}(ℝⁿ;M_{m×m})$ is the generating distribution of an i.d.c.s. if and only if the operator $∂_{t} ⊗ _{m×m} - G∗ $ on $ℝ^{1+n}$ satisfies the Petrovskiĭ condition for forward evolution. Some consequences are discussed.
LA - eng
KW - one-parameter convolution semigroup of rapidly decreasing distributions; partial differential operator with constant coefficients; Cauchy problem; fundamental solution with support in a halfspace; Petrovskiĭ condition; slowly increasing function
UR - http://eudml.org/doc/283529
ER -