High-Dimensional Commuting Polynomial Mappings as Extended Chebyshev Polynomials(Theory)
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- Ishii Masaharu
- School of Modern Management, Sugiyama Jogakuen University
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- Yoshimoto Akinori
- School of Modern Management, Sugiyama Jogakuen University
Bibliographic Information
- Other Title
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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.
Journal
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- Transactions of the Japan Society for Industrial and Applied Mathematics
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Transactions of the Japan Society for Industrial and Applied Mathematics 25 (2), 59-90, 2015
The Japan Society for Industrial and Applied Mathematics
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Details 詳細情報について
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- CRID
- 1390001205768725120
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- NII Article ID
- 110009975768
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- NII Book ID
- AN10367166
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- ISSN
- 09172246
- 24240982
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- NDL BIB ID
- 026600636
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- Text Lang
- ja
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- Data Source
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- JaLC
- NDL
- CiNii Articles
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- Abstract License Flag
- Disallowed