In this paper, we consider the robust stabilization problem for linear time varying (LTV) systems using the gap metric. In particular, we show that the time varying (TV) directed gap reduces to an operator with a TV Hankel plus Toeplitz structure. Computation of the norm of such an operator can be carried out using an iterative scheme involving a TV Hankel operator defined on a space of Hilbert...

Abstract We give a new class of equivalent norms for modulation spaces by replacing the window short-time Fourier transform Hilbert–Schmidt operator. The main result is applied to Cohen’s time-frequency distributions, Weyl operators and localization operators. In particular, any positive distribution with Schwartz kernel can be used an norm spaces. also obtain description as Wiener amalgam oper...

Abstract: The classical Weyl-von Neumann theorem states that for any selfadjoint operator A in a separable Hilbert space H there exists a (non-unique) Hilbert-Schmidt operator C = C∗ such that the perturbed operator A + C has purely point spectrum. We are interesting whether this result remains valid for non-additive perturbations by considering self-adjoint extensions of a given densely define...

Underspread and overspread operators are Hilbert–Schmidt operators with strictly bandlimited Kohn–Nirenberg symbols. In this paper, we prove a classical conjecture concerning the necessity of the underspread condition for the identifiability of such operator classes, and, in doing so, we exhibit a new uncertainty principle phenomenon in the time-frequency analysis of operators.

We construct a natural co-Riemannian structure on the manifold of smooth loops in a Riemannian manifold. We show that the smooth loop space of a stringmanifold is a per-Hilbert–Schmidt locally equivalent co-spin manifold and thus admits a Dirac operator.

Given a complex manifold M endowed with a hermitian metric g and supporting a smooth probability measure μ, there is a naturally associated Dirichlet form operator A on L(μ). If b is a function in L(μ) there is a naturally associated Hankel operator Hb defined in holomorphic function spaces over M . We establish a relation between hypercontractivity properties of the semigroup e−tA and boundedn...

This paper studies the construction of a refinement kernel for a given operator-valued reproducing kernel such that the vector-valued reproducing kernel Hilbert space of the refinement kernel contains that of the given kernel as a subspace. The study is motivated from the need of updating the current operator-valued reproducing kernel in multi-task learning when underfitting or overfitting occu...

The operator-Schmidt decomposition is useful in quantum information theory for quantifying the nonlocality of bipartite unitary operations. We construct a family of unitary operators on C ⊗ C whose operatorSchmidt decompositions are computed using the discrete Fourier transform. As a corollary, we produce unitaries on C ⊗ C with operatorSchmidt number S for every S ∈ {1, ..., 9}. This corollary...