On construction of continuous functions with cusp singularities (Q1409295)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On construction of continuous functions with cusp singularities |
scientific article; zbMATH DE number 1990105
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On construction of continuous functions with cusp singularities |
scientific article; zbMATH DE number 1990105 |
Statements
On construction of continuous functions with cusp singularities (English)
0 references
12 October 2003
0 references
For each function \(s\) from \(\mathbb{R}\) to \([0,\infty]\), which is the lower limit of a sequence of continuous functions, the author gives various explicit constructions of a function \(f\) whose Hölder exponent is a cusp singularity and equals \(s(x)\) for every \(x\). These constructions include orthonormal wavelets, Weierstrass type function, and spline functions.
0 references
wavelets
0 references
scaling exponents
0 references
singularities
0 references
Weierstrass functions
0 references
spline functions
0 references
Takagi function
0 references
0.7854045629501343
0 references
0.7818461060523987
0 references
0.7818461060523987
0 references
0.7773502469062805
0 references
