一类线性偏微分算子连续线性右逆存在的必要条件

数学物理学报 ›› 2011, Vol. 31 ›› Issue (4): 983-990.

一类线性偏微分算子连续线性右逆存在的必要条件

吴密景|王光

山西大学数学科学学院太原 |030006

收稿日期:2009-08-10 修回日期:2010-10-08 出版日期:2011-08-25 发布日期:2011-08-25
基金资助:
国家自然科学基金(61074048)和山西省回国人员基金资助

A Necessary Condition of some Linear Partial Differential Operator |that Admits a Continuous Linear Right Inverse

WU Mi-Jing, WANG Guang

School of |Mathematical Science, Shanxi University, Taiyuan 030006

Received:2009-08-10 Revised:2010-10-08 Online:2011-08-25 Published:2011-08-25
Supported by:
国家自然科学基金(61074048)和山西省回国人员基金资助

摘要/Abstract

摘要：

该文利用Phragmén-Lindel\"{o}f条件和d -拟齐次概念对于S(D)=P(D)-∂²/∂²_n+1^）型算子进行了讨论, 给出了其连续线性右逆存在的一个必要条件.

关键词: 连续线性右逆, Phragmén-Lindel\"{o}f条件, d -拟齐次多项式

Abstract:

In the paper, the linear partial differential operator S(D=P(D)-∂²/∂²_n+1) is disscused by using Phragmén-Lindel\"{o}f condition and d-quasihomogeneous polynomials, and a necessary condition of it, for which the continuous linear right inverse exists, is given.

Key words: Continuous linear right inverse, Phragmén-Lindel\"{o}f condition, , d-quasihomogeneous polynomials

中图分类号:

46F05

吴密景, 王光 . 一类线性偏微分算子连续线性右逆存在的必要条件[J]. 数学物理学报, 2011, 31(4): 983-990.

WU Mi-Jing, WANG Guang . A Necessary Condition of some Linear Partial Differential Operator |that Admits a Continuous Linear Right Inverse[J]. Acta mathematica scientia,Series A, 2011, 31(4): 983-990.

参考文献

[1] H\"{o}mander L. On the existence of rear analytic solutions of partial differential equations with constant coefficients. Invent Math, 1973, 21: 151--183

[2] Meise R, Taylor B A, Vogt D. Characterization of the linear partial differential operators with constant coefficients that admidt a continuous linear right inverse. Ann Inst Fourier (Grenoble), 1990, 40: 619--655

[3] Meie R, Taylor B A, Vogt D. Continuous linear right inverses for partial differential operators on non-quasiaualytic classes and on ultradistributions. Math Nachr, 1996, 180: 449--464

[4] Meie R, Taylor B A, Vogt D. Phragmén-Lindel\"{o}f principles on algebraic varieties. J Amer Math Soc, 1998, 11: 1--39

[5] Braun R W, Meise R, Taylor B A. Algebraic varieties on which the classical Phragmén-Lindel\"{o}f estimates hold for plurisubharmonic functions. Math Z, 1999, 232: 103--135

[6] Braun R W, Meise R, Taylor B A. The geometry of analytic varieties satisfying the local Phragmén-Lindel\"{o}f condition and a geometoc characterization of the partial differential operators that are surjective on A(R)⁴. Trans Amer Soc, 2004, 356: 1315--1383

[7] Palamodov V P. A Criterion for Splitness of Differential Complexes with Constant Coeficients//C.A.Beren- stein, D.C.Struppa.
Geometrical and Algebraical Aspects in Several Complex Variables. EditEl, 1991: 265--291

[8] Bonet J, Nacinnovovich M. Overdetermined Cauchy problem in some classes of ultradifferentiable functions. Ann Math Pura Appl, 2001, 180: 81--126

[9] Braun R W, Meise R, Taylor B A. Characterizatio of the homogeneus polynomials P for which (P+Q)(D) admits a continuous linear right inverse for all pertubations Q. Pacific J Math, 2000, 192: 201--218

[10] Braun R W, Meise R, Taylor B A. Pertubation of differential operators admitting acontinuous linear right inverse on ultradistributions. Pacific J Math, 2003, 212: 25--48

[11] H\"{o}mander L. An Introduction to Complex Analysis in Several Variables. Amsterdam: Elsevier Science Publishers B V, 1990