Polynomial projectors preserving homogeneous partial differential equations |
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| Authors: | Dinh-D&#x ng, Jean-Paul Calvi,Nguyê n Tiê n Trung |
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| Affiliation: | aInformation Technology Institute, Vietnam National University, Hanoi, E3, 144 Xuan Thuy Rd., Cau Giay, Hanoi, Vietnam;bLaboratoire de Mathématiques E. Picard, UFR MIG, Université Paul Sabatier, 31062 Toulouse Cedex, France |
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| Abstract: | A polynomial projector Π of degree d on is said to preserve homogeneous partial differential equations (HPDE) of degree k if for every and every homogeneous polynomial of degree k, q(z)=∑|α|=kaαzα, there holds the implication: q(D)f=0q(D)Π(f)=0. We prove that a polynomial projector Π preserves HPDE of degree if and only if there are analytic functionals with such that Π is represented in the following form with some , where uα(z)zα/α!. Moreover, we give an example of polynomial projectors preserving HPDE of degree k (k1) without preserving HPDE of smaller degree. We also give a characterization of Abel–Gontcharoff projectors as the only Birkhoff polynomial projectors that preserve all HPDE. |
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| Keywords: | Polynomial projector preserving homogeneous partial differential equations Space of interpolation conditions D-Taylor projector Birkhoff projector Abel– Gontcharoff projector |
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