## On a variational approach to truncated problems of moments.(English)Zbl 1274.44010

The author considers a problem of finding an a.e. non-negative function $$f$$ on a closed set $$T\subset \mathbb R^n$$ such that $$\int _T | t^i| f(t) dt < \infty$$ and $$\int _T t^i f(t) dt = g_i$$, $$i\in I$$, where $$(g_i)_{i\in I}$$ is a prescribed set of numbers, $$g_0 = 1$$ and $$I\subset \mathbb Z^n_+$$. Under some conditions on $$T$$ and $$I$$, the existence of $$f$$ is shown to be equivalent to the condition that a functional $$L$$ (Lagrangian) is bounded from above and $$\sup L$$ is attained at a (unique) point.

### MSC:

 44A60 Moment problems 30E05 Moment problems and interpolation problems in the complex plane

### Keywords:

moment problem; representing measure; Lagrangian
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