Weiss Conjectures

In order to study the behaviour of physical systems governed by partial differential equations subjected to forcing, the classical approach is to represent them as linear ordinary differential equations which evolve on an infinite dimensional function space. A fundamental class of problems in this area are known as Weiss Conjectures which ask whether certain input-output properties of controlled infinite dimensional systems can by characterised by a purely frequency-domain condition. The truth of the Weiss Conjecture for different classes of underlying operator has fascinating links to the theory of spaces of analytic functions. 

wc.jpg

Related Publications

  • Jacob B, Partington JR, Pott S, Wynn A, 2018, beta-admissibility of observation operators for hypercontractive semigroups, Journal of Evolution Equations, 18, 153-170. Link. 

  • Jacob B., Rydhe E., Wynn A., 2014, The weighted Weiss conjecture and reproducing kernel theses for generalized Hankel operators, Journal of Evolution Equations, 14, 85-120. Link.

  • Wynn A, 2011, Sufficient conditions for weighted admissibility of operators with applications to Carleson measures and multipliers,Quarterly Journal of Mathematics, 62, 747-770. Link.

  • Wynn A, 2010, alpha-Admissibility of observation operators in discrete and continuous time, Complex Analysis and Operator Theory, 4, 109-131. Link. 

  • Wynn A, 2009, Counterexamples to the discrete and continuous weighted Weiss conjectures, SIAM Journal on Control and Optimization, 48, 2620-2635. Link. 

  • Wynn A., 2009, alpha-admissibility of the right-shift semigroup on L-2(R+), Systems & Control Letters, 58, 677-681. Link.