Algebras of Convolution Type Operators with Continuous Data do Not Always Contain All Rank One Operators

Operators with Singular Continuous Spectrum: Ii. Rank One Operators

For an operator, A, with cyclic vector φ, we study A+ λP where P is the rank one projection onto multiples of φ. If [α,β] ⊂ spec(A) and A has no a.c. spectrum, we prove that A + λP has purely singular continuous spectrum on (α, β) for a dense Gδ of λ’s. §

DCCO: Towards Deformable Continuous Convolution Operators

Discriminative Correlation Filter (DCF) based methods have shown competitive performance on tracking benchmarks in recent years. Generally, DCF based trackers learn a rigid appearance model of the target. However, this reliance on a single rigid appearance model is insufficient in situations where the target undergoes non-rigid transformations. In this paper, we propose a unified formulation fo...

Continuityof Operators Intertwiningwith Convolution Operators

Let G be a locally compact abelian group, let m be a bounded complex-valued Borel measure on G; and let Tm be the corresponding convolution operator on LðGÞ: Let X be a Banach space and let S be a continuous linear operator on X : Then we show that every linear operator F : X ! LðGÞ such that FS 1⁄4 TmF is continuous if and only if the pair ðS;TmÞ has no critical eigenvalue. # 2002 Elsevier Sci...

Rank one perturbations of self-adjoint operators

Generalized Continuous Frames for Operators

In this note, the notion of generalized continuous K- frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized continuous $K$-frames. A necessary and sufficient condition for the existence of a generalized continuous $K$-frame in terms of its frame operator is obtained and a characterization of a generalized continuous $K$-frame for $ mathcal{H} $ wi...