Peano kernel associated with the polyharmonic mean value property in the annulus

The well known mean value property for polyharmonic functions in the ball (see Picone [9], Bramble-Payne [2]) is generalized to the case of an annular domain. We prove that the Peano kernel arising from this new mean value property has definite sign. It is a polyspline in the sense of [8]. The prese...

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Bibliographic Details
Published inNumerical functional analysis and optimization Vol. 21; no. 5-6; pp. 683 - 692
Main Authors Haußmann, Werner, Kounchev, Ognyan
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Marcel Dekker, Inc 01.01.2000
Taylor & Francis
Subjects
Exact sciences and technology
Finite differences and functional equations
Functional analysis
Mathematical analysis
Mathematics
Sciences and techniques of general use
Special functions
Polyharmonic function
Functional analysis
Differential operator
Mean value
Spline
Finite difference functional
Peano kernel
Finite difference method
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Summary:The well known mean value property for polyharmonic functions in the ball (see Picone [9], Bramble-Payne [2]) is generalized to the case of an annular domain. We prove that the Peano kernel arising from this new mean value property has definite sign. It is a polyspline in the sense of [8]. The present results generalize former investigations concerning the Peano kernel associated with the mean value property of polyharmonic functions in the ball.
ISSN:0163-0563
1532-2467
DOI:10.1080/01630560008816980