ABSTRACT

The theory of distributions is most often presented as L. Schwartz originally presented it: as a theory of the duality of topological vector spaces. Although this is a sound approach, it can be difficult, demanding deep prior knowledge of functional analysis. The more elementary treatments that are available often consider distributions as limits o

chapter 1|22 pages

DEFINITIONS AND PRELIMINARIES

THEOREM PROOF.

chapter 1|2 pages

DEFINITIONS AND PRELIMINARIES (1.13.1) .

chapter |2 pages

A • "

chapter |1 pages

PROOF.

chapter |44 pages

OF THEOREM

PROOF

chapter |4 pages

PROOF.

TO this end we have to show that

chapter |19 pages

THEOREM

chapter |3 pages

DEFINITION

chapter |8 pages

EXAMPLE

chapter |11 pages

EXAMPLE

chapter |6 pages

THEOREM

chapter 6|2 pages

TEMPERED DISTRIBUTIONS AND FOURIER TRANSFORMS

exp(-i|a| )^a^(a)

chapter 128|2 pages

7. ORTHOGONAL EXPANSIONS OF DISTRIBUTIONS

chapter 7|7 pages

. ORTHOGONAL EXPANSIONS OP DISTRIBUTIONS

chapter |13 pages

COROLLARY