# Behavior of biharmonic functions on Wiener's and Royden's compactifications

Y. K. Kwon; Leo Sario; Bertram Walsh

Annales de l'institut Fourier (1971)

- Volume: 21, Issue: 3, page 217-226
- ISSN: 0373-0956

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topKwon, Y. K., Sario, Leo, and Walsh, Bertram. "Behavior of biharmonic functions on Wiener's and Royden's compactifications." Annales de l'institut Fourier 21.3 (1971): 217-226. <http://eudml.org/doc/74049>.

@article{Kwon1971,

abstract = {Let $R$ be a smooth Riemannian manifold of finite volume, $\Delta $ its Laplace (-Beltrami) operator. Canonical direct-sum decompositions of certain subspaces of the Wiener and Royden algebras of $R$ are found, and for biharmonic functions (those for which $\Delta \Delta u = 0$) the decompositions are related to the values of the functions and their Laplacians on appropriate ideal boundaries.},

author = {Kwon, Y. K., Sario, Leo, Walsh, Bertram},

journal = {Annales de l'institut Fourier},

language = {eng},

number = {3},

pages = {217-226},

publisher = {Association des Annales de l'Institut Fourier},

title = {Behavior of biharmonic functions on Wiener's and Royden's compactifications},

url = {http://eudml.org/doc/74049},

volume = {21},

year = {1971},

}

TY - JOUR

AU - Kwon, Y. K.

AU - Sario, Leo

AU - Walsh, Bertram

TI - Behavior of biharmonic functions on Wiener's and Royden's compactifications

JO - Annales de l'institut Fourier

PY - 1971

PB - Association des Annales de l'Institut Fourier

VL - 21

IS - 3

SP - 217

EP - 226

AB - Let $R$ be a smooth Riemannian manifold of finite volume, $\Delta $ its Laplace (-Beltrami) operator. Canonical direct-sum decompositions of certain subspaces of the Wiener and Royden algebras of $R$ are found, and for biharmonic functions (those for which $\Delta \Delta u = 0$) the decompositions are related to the values of the functions and their Laplacians on appropriate ideal boundaries.

LA - eng

UR - http://eudml.org/doc/74049

ER -

## References

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- [6] G. DE RHAM, Variétés différentiables, Hermann, Paris, (1960), 196 p. Zbl0089.08105
- [7] L. SARIO — M. NAKAI, Classification theory of Riemann surfaces, Springer, (1970), 446 p. Zbl0199.40603MR41 #8660
- [8] L. SARIO — M. SCHIFFER — M. GLASNER, The span and principal functions in Riemannian spaces, J. Analyse Math. 15 (1965), 115-134. Zbl0136.09603MR32 #1655
- [9] I.N. VEKUA, New methods for solving elliptic equations, North-Holland, Amsterdam, (1967), 358 p. Zbl0146.34301MR35 #3243

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