Abstract
Representation and boundedness properties of linear, right-shift invariant operators on half-line Bessel potential spaces (also known as fractional-order Sobolev spaces) as operator-valued multiplication operators in terms of the Laplace transform are considered. These objects are closely related to the input-output operators of linear, time-invariant control systems. Characterisations of when such operators map continuously between certain interpolation spaces and/or Bessel potential spaces are provided, including characterisations in terms of boundedness and integrability properties of the symbol, also known as the transfer function in this setting. The paper considers the Hilbert space case, and the theory is illustrated by a range of examples.
| Original language | English |
|---|---|
| Article number | 19 |
| Number of pages | 34 |
| Journal | Integral Equations and Operator Theory |
| Volume | 95 |
| Issue number | 3 |
| Early online date | 25 Aug 2023 |
| DOIs | |
| Publication status | Published - Sept 2023 |
Bibliographical note
Funding Information:Chris Guiver’s contribution to this work has been supported by a Personal Research Fellowship from the Royal Society of Edinburgh (RSE). Chris Guiver expresses gratitude to the RSE for the financial support.
Publisher Copyright:
© 2023, The Author(s).
Keywords
- Bessel potential space
- Fractional-order Sobolev space
- Input–output operator
- Interpolation space
- Laplace transform
- Mathematical systems and control theory
- Multiplier theorem
- Paley–Wiener Theorem
- Shift-invariant operator
- Wiener-Hopf integral operator
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory