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arXiv · 1609.04540

Around operators not increasing the degree of polynomials

T. Augusta Mesquita·P. Maroni
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Abstract

We present a generic operator $J$ simply defined as a linear map not increasing the degree from the vectorial space of polynomial functions into itself 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. It is also provided examples where the results are applied to the case where $J$'s expansion is limited to three terms.

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T. Augusta Mesquita, P. Maroni. 2016-09-15. Around operators not increasing the degree of polynomials. https://arxiv.org/abs/1609.04540

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