Direct methods in the calculus of variations
Direct methods in the calculus of variations
On some indeterminate moment problems for measures on a geometric progression
Journal of Computational and Applied Mathematics
| Hi-index | 0.00 |
Different notions of convexity that arise in several problems within the calculus of variations are briefly revised. We derive some particular stability properties for convex functions being homogeneous of degree one. Stability is investigated in the sense of convexity being conserved when modifying the considered functions in a special analytic or algebraic way. Criteria on functions for being rank-one convex are stated and elaborated in the case of orthogonal polynomials. This leads to the observation that highly non-trivial convexity properties are to be expected in the case of special orthogonal polynomials. The obtained particular results might give further insight into connections between variational calculus and special functions.