An imbedding space for Schwartz distributions

Pointwise Kernels of Schwartz Distributions

We show that Schwartz distributions have kernels in the class of the pointwise nonstandard functions. The main purpose of this note is to show that every Schwartz distribution T G 3' has a kernel /: *Rd —> *C in the class of the pointwise nonstandard functions in the sense that (1) (T,p)= [ f(xy<p(x)dx for all <p G 3, where *<p is the nonstandard extension of (p. Recall that, in general, the Sc...

On Extension of Schwartz Distributions to the Space of Discontinuous Test Functions

The present paper is devoted to the investigation of the properties of the space R of distributions with discontinuous test functions of several variables. The consideration of the discontinuous test functions allows us to define the correct operations (i.e., the operations which are defined everywhere, continuous and coincident with the ordinary ones for the regular distributions) of integrati...

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

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...