| Abstract: | The problem of Hermite operator interpolation with interpolational conditions containing Gateaux higher-order differentials in arbitrary directions is investigated. A necessary and sufficient condition for solvability of this problem in a Hilbert space is established, and the set of all Hermite operator polynomials and its subset of interpolants preserving operator polynomials of the same degree are described. Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 78, 1994, pp. 38–48. |
