On manifolds of eigenfunctions and potentials generated by a family of periodic boundary-value problems
We consider a family of boundary-value problems with some potential as a parameter. We study the manifold of normalized eigenfunctions with even number of zeros in a period, and the manifold of potentials associated with double eigenvalues. In particular, we prove that the manifold of normalized eigenfunctions is a trivial fiber space over a unit circle and that the manifold of potentials with double eigenvalues is a homotopically trivial manifold trivially imbedded into the space of potentials.
English version (Springer): Ukrainian Mathematical Journal 48 (1996), no. 6, pp 866-879.
Citation Example: Dymarskii Ya. M. On manifolds of eigenfunctions and potentials generated by a family of periodic boundary-value problems // Ukr. Mat. Zh. - 1996. - 48, № 6. - pp. 771-781.