Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4616068 | Journal of Mathematical Analysis and Applications | 2014 | 13 Pages |
Abstract
In the table (on p. 442) of John Horváth's textbook “Topological Vector Spaces and Distributions”, the questions for an explicit description of the topology of OCm by seminorms, for the completeness and for the metrizability of the space OCm remained open, whereas, for m=â, the completeness was shown by A. Grothendieck in his thesis. We resolve these questions in Proposition 1, Proposition 2, Proposition 3. In Proposition 4, Proposition 5, Proposition 6, Proposition 7, we investigate multiplication and convolution in the spaces Sm, OCm, Sâ²m, OCâ²m analogously to the treatment in the spaces Em, Dm, Dâ²m, Eâ²m in J. Horváth's book (Ch. 4, §6 Multiplication, §9 Convolution, §10 Regularization). In Section 6, the multiplication and convolution of holomorphic functions with values in Sm, OCm, Sâ²m, OCâ²m are investigated analogously to J. Horváth's treatment of holomorphic functions with values in the spaces Em, Dm, Dâ²m, Eâ²m.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Norbert Ortner, Peter Wagner,