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Mean value properties of generalised eigenfunctions†

Published online by Cambridge University Press:  20 January 2009

Eberhard Gerlach
Eberhard Gerlach
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver 168, B.C.
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Some Hilbert spaces of continuous functions satisfying a mean value property are studied in which the generalised eigenfunctions of any selfadjoint operator again satisfy the same mean value property. Applications are made to nullspaces of some differential operators. The classes of functions involved in these applications are less general than those studied by K. Maurin (6); however, the Hilbert space norms may be arbitrary, while Maurin only considered L2-norms.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 2 , December 1970 , pp. 155 - 158
Copyright
Copyright © Edinburgh Mathematical Society 1970

References

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