Image of the Schwartz space under spectral projection

On the Schwartz Space of the Basic Affine Space

Let G be the group of points of a split reductive algebraic group G over a local field k and let X = G/U where U is the group of k-points of a maximal unipotent subgroup of G. In this paper we construct certain canonical G-invariant space S(X) (called the Schwartz space of X) of functions on X , which is an extension of the space of smooth compactly supported functions on X . We show that the s...

Hubble Space Telescope Imaging of the Schwartz

Schwartz 82 (IM Lupi; HBC 605; IRAS 15528-3747) is an M0 T Tauri star located within the Lupus star forming clouds at a distance of ∼190 pc (Wichmann et al. 1998). It is one of four young stellar objects in a small CO(1-0) core near the extreme T Tauri star RU Lupi (Tachihara et al. 1996). Unlike its more famous neighbor, Sz 82 displays only a modest amount of emission-line activity, with an Hα...

The Schwartz space and the Fourier transform

Parametric image reconstruction using spectral analysis of PET projection data.

Spectral analysis is a general modelling approach that enables calculation of parametric images from reconstructed tracer kinetic data independent of an assumed compartmental structure. We investigated the validity of applying spectral analysis directly to projection data motivated by the advantages that: (i) the number of reconstructions is reduced by an order of magnitude and (ii) iterative r...

Multi-spectral Image Analysis Based on Dynamical Evolutionary Projection Pursuit

Principal component analysis (PCA) is usually used for compressing information in multivariate data sets by computing orthogonal projections that maximize the amount of data variance. PCA is effective if the multivariate data set is a vector with Gaussian distribution. But multi-spectral images data sets are not probably submitted to such Gaussian distribution. The paper proposes a method based...