Representations and Regularity of Vector-Valued Right-Shift Invariant Operators Between Half-Line Bessel Potential Spaces

Abstract Representation and boundedness properties of linear, right-shift invariant operators on half-line Bessel potential spaces (also known as fractional-order Sobolev spaces) operator-valued multiplication in terms the Laplace transform are considered. These objects closely related to input–output time-invariant control systems. Characterisations when such map continuously between certain interpolation and/or provided, including characterisations integrability symbol, also transfer function this setting. The paper considers Hilbert space case, theory is illustrated by a range examples.