The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Approximation of translation invariant operators”

Periodic solutions of degenerate differential equations in vector-valued function spaces

Carlos Lizama, Rodrigo Ponce (2011)

Studia Mathematica

Similarity:

Let A and M be closed linear operators defined on a complex Banach space X. Using operator-valued Fourier multiplier theorems, we obtain necessary and sufficient conditions for the existence and uniqueness of periodic solutions to the equation d/dt(Mu(t)) = Au(t) + f(t), in terms of either boundedness or R-boundedness of the modified resolvent operator determined by the equation. Our results are obtained in the scales of periodic Besov and periodic Lebesgue vector-valued spaces. ...

Periodic solutions of an abstract third-order differential equation

Verónica Poblete, Juan C. Pozo (2013)

Studia Mathematica

Similarity:

Using operator valued Fourier multipliers, we characterize maximal regularity for the abstract third-order differential equation αu'''(t) + u''(t) = βAu(t) + γBu'(t) + f(t) with boundary conditions u(0) = u(2π), u'(0) = u'(2π) and u''(0) = u''(2π), where A and B are closed linear operators defined on a Banach space X, α,β,γ ∈ ℝ₊, and f belongs to either periodic Lebesgue spaces, or periodic Besov spaces, or periodic Triebel-Lizorkin spaces.