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Around operators not increasing the degree of polynomials |
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| Authors: | T Augusta Mesquita P Maroni |
| Institution: | 1. Instituto Politécnico de Viana do Castelo, Viana do Castelo, Portugal;2. Centro de Matemática, Univ. do Porto, Porto, Portugal;3. CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, Paris, France;4. UPMC Univ Paris 06, UMR 7598, Lab. Jacques-Louis Lions, Paris, France |
| Abstract: | We present a generic operator J defined on the vectorial space of polynomial functions and we address the problem of finding the polynomial sequences that coincide with the (normalized) J-image of themselves. The technique developed assembles different types of operators and initiates with a transposition of the problem to the dual space. We provide examples for a J limited to three terms. |
| Keywords: | Classical orthogonal polynomials differential operators Appell polynomial sequences two-orthogonal polynomials |