Chúng tôi cung cấp cho một cuộc khảo sát ngắn gọn trên một phương pháp tiếp cận mới trong nghiên cứu của máy chiếu đa thức bảo toàn đồng nhất một phần phương trình vi phân hoặc quan hệ khác biệt giữa đồng nhất, và các tài sản của họ suy về không gian của điều kiện suy. | Vietnam Journal of Mathematics 34 3 2006 241-254 Viet n a m J 0 u r n a I of MATHEMATICS VAST 2006 Survey Interpolation Conditions and Polynomial Projectors Preserving Homogeneous Partial Differential Equations Dinh Dung Information Technology Institute Vietnam National University Hanoi E3 144 Xuan Thuy Rd. Cau Giay Hanoi Vietnam Dedicated to the 70th Birthday of Professor V. Tikhomirov Received October 7 2005 Revised August 14 2006 Abstract. We give a brief survey on a new approach in study of polynomial projectors that preserve homogeneous partial differential equations or homogeneous differential relations and their interpolation properties in terms of space of interpolation conditions. Some well-known interpolation projectors as Abel-Gontcharoff Birkhoff and Kergin interpolation projectors are considered in details. 2000 Mathematics Subject Classification 41A05 41A63 46A32. Keywords Polynomial projector preserving homogeneous partial differential equations polynomial projector preserving homogeneous differential relations space of interpolation conditions Ì-T aylor projector Birkhoff projector Abel-Gontcharoff projector Kergin projector. 1. Introduction . We begin with some preliminary notions. Let us denote by H Cn the space of entire functions on Cn equipped with its usual compact convergence topology and Pd Cn the space of polynomials on Cn of total degree at most d. A polynomial projector of degree d is defined as a continuous linear map n from 242 Dinh Dung H Cn into Pd Cn for which n p p Vp e d c . Let H Cn denote the space of linear continuous functionals on H Cn whose elements are usually called analytic functionals. We define the space I n c H Cn as follows an element p G H Cn belongs to I n if and only if for any f G H Cn we have p f p n f . This space is called space of interpolation conditions for n. Let pa a d be a basis of Pd Cn whose elements are enumerated by the multi-indexes a oi . ad G Z with length a ai an not greater than d. Then there .
