On the Cauchy problem for convolution equations

• Języki publikacji: EN

Abstrakty

EN

We consider one-parameter (C₀)-semigroups of operators in the space $𝓢'(ℝⁿ;ℂ^{m})$ with infinitesimal generator of the form $(G*)|_{𝓢'(ℝⁿ;ℂ^{m})}$ where G is an $M_{m×m}$-valued rapidly decreasing distribution on ℝⁿ. It is proved that the Petrovskiĭ condition for forward evolution ensures not only the existence and uniqueness of the above semigroup but also its nice behaviour after restriction to whichever of the function spaces $𝓢(ℝⁿ;ℂ^{m})$, $𝓓_{L^{p}}(ℝⁿ;ℂ^{m})$, p ∈ [1,∞], $(𝓞_{a})(ℝⁿ;ℂ^{m})$, a ∈ ]0,∞[, or the spaces $𝓓'_{L^{q}}(ℝⁿ;ℂ^{m})$, q ∈ ]1,∞], of bounded distributions.

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: 2013
• Tom: 133
• Numer: 1
• Strony: 115-132

Daty

wydano

2013

Twórcy

Identyfikatory

DOI

10.4064/cm133-1-8