This paper addresses state-space realizations for nonlinear adjoint operators. In particular the relationship among nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are clarified. The characterization of controllability, observability and Hankel operators, and controllability and observability functions will be derived based on it. Furthermore ...

In this paper we show that the theory of Hankel operators in the torus T , for d > 1, presents striking differences with that on the circle T, starting with bounded Hankel operators with no bounded symbols. Such differences are circumvented here by replacing the space of symbols L∞(T) by BMOr(T), a subspace of product BMO, and the singular numbers of Hankel operators by so-called sigma numbers....

The classical time-invariant Hankel-norm approximation problem is generalized to the time-varying context. The input-output operator of a time-varying bounded causal linear system acting in discrete time may be specified as a bounded upper-triangular operator T with block matrix entries Tij. For such an operator T, we will define the Hankel norm as a generalization of the time-invariant Hankel ...

Abstract Tracy and Widom showed that fundamentally important kernels in random matrix theory arise from systems of differential equations with rational coefficients. More generally, this paper considers symmetric Hamiltonian systems and determines the properties of kernels that arise from them. The inverse spectral problem for self-adjoint Hankel operators gives sufficient conditions for a self...

This paper provides a new proof of the index formula for block Toeplitz operators. The idea is to calculate a certain integral formula for the winding number using Fourier series, expressing this in terms of Hankel operators, and producing the expected index.

In dynamic contrast enhanced (DCE) MRI, temporal and spatial resolution can be improved by timeresolved angiography with interleaved stochastic trajectories (TWIST). However, due to view sharing, the temporal resolution of TWIST is not a true one. To overcome this limitation, we employ recently proposed annihilating filter-based low rank Hankel matrix approach (ALOHA) that interpolates the miss...

Abstract. Using Hankel operators and shift-invariant subspaces on Hilbert space, this paper develops the theory of the operators associated with soft and hard edges of eigenvalue distributions of random matrices. Tracy and Widom introduced a projection operator W to describe the soft edge of the spectrum of the Gaussian unitary ensemble. The subspace WL is simply invariant under the translation...

Recall that the Lorentz ideal C− p is the collection of operators A satisfying the condition ‖A‖p = ∑∞ j=1 j sj(A) < ∞. Consider Hankel operators Hf : H(S) → L(S, dσ) H(S), where H(S) is the Hardy space on the unit sphere S in C. In this paper we characterize the membership Hf ∈ C− p , 2n < p <∞.