High-Dimensional Commuting Polynomial Mappings as Extended Chebyshev Polynomials(Theory)

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  • Chebyshev多項式を拡張した高次元可換多項式写像(理論)
  • Chebyshev多項式を拡張した高次元可換多項式写像
  • Chebyshev タコウシキ オ カクチョウ シタ コウジゲン カカンタコウシキ シャゾウ

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Abstract

We extend Chebyshev polynomials to three types of n-dimensional polynomial mappings (C^n→C^n), by defining analogues of m-times angle formulas of trigonometric functions, keeping commutativity and recursion expressions. We prove that two types of them have properties of being systems of eigen functions, orthogonalities and invariances of mapping like original Chebyshev polynomials. However, they do not have completeness as basises of the space of continuous functions. Moreover we state a relation between three types of them and extended Dickson polynomials.

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