Name
Abstract | ||
|---|---|---|
We consider the Markov problem of finding the so-called Markov factor M(U,K):=supu∈U‖Du‖‖u‖, of the set of differentiable functions U, where Du:=|∂u|ℓ2 stands for the ℓ2-norm of the gradient vector of u, and ‖⋅‖ is the weighted L2 norm on the set K⊂Rd. In the univariate case exact L2-Markov inequalities are known for algebraic polynomials on the real line, half line and intervals. We outline a variational approach to the above problem and show how this leads either to certain partial differential equations, or to a system of homogeneous linear equations. This method will be illustrated by using it to solve the L2 Markov problem for the cases of d-dimensional spaces and d-dimensional hyperquadrants. In the case of d-spaces the solution is given for homogeneous polynomials, as well. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.jat.2011.11.005 | Journal of Approximation Theory |
Keywords | Field | DocType |
Multivariate polynomial,Markov constant,Variational method,Differential equation,Eigenvalue of a matrix | Linear equation,Combinatorics,Mathematical optimization,Algebraic number,Polynomial,Real line,Mathematical analysis,Markov chain,Markov's inequality,Differentiable function,Norm (mathematics),Mathematics | Journal |
Volume | Issue | ISSN |
164 | 3 | 0021-9045 |
Citations | PageRank | References |
1 | 0.48 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| András Kroó | 1 | 15 | 7.29 |
| József Szabados | 2 | 2 | 1.54 |