Direct and inverse problems for vector logarithmic potentials with external fields

  • A. I. Aptekarev
  • M. A. Lapik
  • V. G. LysovEmail author


We consider extremal problems for the energy of the logarithmic potential with external fields closely related with the inverse spectral problem method. The method is based on the relations between the external field and the supports of the equilibrium measures which were discovered in the pioneering papers of Rakhmanov, Saff, Mhaskar and Buyarov (RSMB-method). We propose a generalization of the RSMB-method for the vector of measures with matrix of interaction between components.


Logarithmic potential Energy with external field Hermite-Padé approximants Extremal and Equilibrium measure Hyperbolic PDEs 

Mathematics Subject Classification

Primary 41A20 41A21 41A10 Secondary 47B99 30B70 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  1. 1.Keldysh Institute for Applied MathematicsRussian Academy of Sciences and Moscow State UniversityMoscowRussia
  2. 2.Keldysh Institute of Applied MathematicsRussian Academy of SciencesMoscowRussia

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