带有非Carleman位移的奇异积分算子的Noether性质

来源期刊：中南大学学报(自然科学版)1988年第4期

论文作者：吕德

文章页码：453 - 458

关键词：奇异积分算子； 紧算子； 位移边界

Key words：singular integral operator； compact operator； displacement boundary

摘    要：本文讨论带有非Carleman位移的奇异积分算子K的Noether性质。借助于四个非积分算子A_±和B_±,把研究算子K归结为研究算子A_±和B_±。在对位移α(t)作不同的假设条件下,文中得到了空间L_P(Г)中算子A_±和B_±的Noether条件,从而给出算子K的Noether性充分条件。

Abstract: The main purpose of this paper is to discuss the Noether′s property of singular integraloperator K with non-Carleman′s shift.With the help of four non-integral operators A_± nd B_±,the Noether′s property of K is reduced to the corresponding property of A_± and B_± n our study.Based on various hypotheses for displacement a(t),we obtain the Noether′s onditions of A_± and B_± in space L_p(Г)and thereby find out sufficient conditions of Noether′s roperty for operatorK.