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

• Języki publikacji: EN

Abstrakty

EN

The paper is devoted to infinitely differentiable one-parameter convolution semigroups in the convolution algebra $𝓞'_{C}(ℝⁿ;M_{m×m})$ of matrix valued rapidly decreasing distributions on ℝⁿ. It is proved that $G ∈ 𝓞'_{C}(ℝⁿ;M_{m×m})$ is the generating distribution of an i.d.c.s. if and only if the operator $∂_{t} ⊗ 𝟙_{m×m} - G∗ $ on $ℝ^{1+n}$ satisfies the Petrovskiĭ condition for forward evolution. Some consequences are discussed.

Kategorie tematyczne

• 47D06: One-parameter semigroups and linear evolution equations
• 42B99: None of the above, but in this section
• 46F99: None of the above, but in this section
• 35E15: Initial value problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 128
• Numer: 1
• Strony: 49-68

Daty

wydano

2012

Twórcy

Identyfikatory

DOI

10.4064/cm128-1-6