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Explicit and approximate solutions of second order elliptic differential equations in hilbert and banach spaces |
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| Authors: | Ivan P. Gavrilyuk Vladimir L. Makarov |
| Affiliation: | 1. Faculty of Mathematics and Computer Science , University of Leipzig , Augustusplatz 10, Leipzig, 04109, Germany;2. Department of Cybernetics , Kiev University ‘T. Shevtshenko’ , Prospekt Glushkova 6, Kiev-127, 252127, Ukraine |
| Abstract: | An explicit closed-form solution for an abstract elliptic equation in Hilbert or Banach space is presented. Using this explicit representation we propose an approximation with the accuracy automatically depending on the smoothness of the initial data. |
| Keywords: | explicit representation of solutions Cayley transform Meixner polynomials 65N35 65J10 |