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

被引：2

作者：

Guiver, Chris ^{[1
]}

Opmeer, Mark R. ^{[2
]}

机构：

[1] Edinburgh Napier Univ, Sch Comp Engn & Built Environm, Merchiston Campus, Edinburgh, Scotland

[2] Univ Bath, Dept Math Sci, Bath, England

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2023年 / 95卷 / 03期

关键词：

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; QUADRATIC CONTROL-PROBLEM; PRITCHARD-SALAMON; SYSTEMS; INPUT; CONVOLUTION; STABILITY; NORMS;

D O I：

10.1007/s00020-023-02738-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：34