Asymptotic evaluations for multivariate Mellin convolution operators

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...

Asymptotic normality and confidence intervals for inverse regression models with convolution-type operators

We consider inverse regression models with convolution-type operators which mediate convolution on R (d ≥ 1) and prove a pointwise central limit theorem for spectral regularisation estimators which can be applied to construct pointwise confidence regions. Here, we cope with the unknown bias of such estimators by undersmoothing. Moreover, we prove consistency of the residual bootstrap in this se...

Texture Segmentation using Circular-Mellin Operators

Texture is an important preattentive cue in region-based segmentation of images. In this paper, we discuss the use of circular-Mellin features for segmenting an image into homogenous regions. The circular-Mellin operators represent the spectral decomposition of the image scene in the polar-log coordinate system and are invariant to both scale and orientation of the target. Coupled with the uniq...

Uniform Lorentz norm estimates for convolution operators

Uniform endpoint Lorentz norm improving estimates for convolution operators with affine arclength measure supported on simple plane curves are established. The estimates hold for a wide class of simple curves, and the condition is stated in terms of averages of the square of the affine arclength weight, extending previously known results. MSC: Primary 44A35; secondary 42B35

Inequalities for Strongly Singular Convolution Operators