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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| Published in | Numerical functional analysis and optimization Vol. 21; no. 5-6; pp. 683 - 692 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia, PA
Marcel Dekker, Inc
01.01.2000
Taylor & Francis |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Kounchev, Ognyan Haußmann, Werner |
| Author_xml | – sequence: 1 givenname: Werner surname: Haußmann fullname: Haußmann, Werner organization: Department of Mathematics , Gerhard-Mercator-University – sequence: 2 givenname: Ognyan surname: Kounchev fullname: Kounchev, Ognyan organization: Department of Mathematics , Bulgarian Academy of Sciences |
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| Cites_doi | 10.1090/S0002-9947-98-01961-8 10.2307/2313762 10.1007/978-94-011-5036-1_15 |
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| Issue | 5-6 |
| Keywords | Polyharmonic function Functional analysis Differential operator Mean value Spline Finite difference functional Peano kernel Finite difference method |
| Language | English |
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| References | Haußmann W. (CIT0005) 1998 Schumaker L. L. (CIT0011) 1981 Pontrjagin L. S. (CIT0010) 1962 CIT0003 CIT0002 Karlin S. (CIT0007) 1966 Aronszajn N. (CIT0001) 1983 CIT0004 Picone M. (CIT0009) 1935; 4 John F. (CIT0006) 1992 CIT0008 |
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| Snippet | 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.... |
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| SubjectTerms | Exact sciences and technology Finite differences and functional equations Functional analysis Mathematical analysis Mathematics Sciences and techniques of general use Special functions |
| Title | Peano kernel associated with the polyharmonic mean value property in the annulus |
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