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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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A continuous linear operator T, on the space of en-tire functions in d variables, is PDE-preserving for a given set P µ C[»1; :::; »d] of polynomials if it maps every kernel-set ker P(D), P 2 P, invariantly. It is clear that the set O(P) of PDE-preserving
operators for P forms an algebra under composition. We study and link properties and structures on the operator side O(P) versus the corresponding family P of polynomials. For our purposes, we intro-duce notions such as the PDE-preserving hull and basic sets for a given set P which, roughly, is the largest, respectively a minimal, collection of polynomials that generate all the PDE-preserving op-erators for P. We also describe PDE-preserving operators via a kernel theorem. We apply Hilbert's Nullstellensatz.
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참고문헌 (7)
참고문헌 신청
/ 1955 / Existence et approximation des solutions des equations auxderivees partielles des equations de convolution : 271 ~ 354
/ 1979. / An introduction to complex analysis in several variables(2rd edi-tion
/ 1990. / The Analysis of Linear Partial Dierential Operators I(2nd edition
/ 2003 / The PDE-preserving operators on the nuclearly entire functions 100 (1-2) : 69 ~ 81
/ 2003 / ^,PDE-Preserving Operators on Smooth Functions 39
/ 1979. / An introduction to complex analysis in several variables(2rd edi-tion
/ 1990. / The Analysis of Linear Partial Dierential Operators I(2nd edition
/ 2003 / The PDE-preserving operators on the nuclearly entire functions 100 (1-2) : 69 ~ 81
/ 2003 / ^,PDE-Preserving Operators on Smooth Functions 39
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