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Spaces of holomorphic functions and Hilbert–Schmidt subspaces

Published online by Cambridge University Press:  18 May 2009

Eberhard Gerlach
Eberhard Gerlach
Affiliation:
University of British Columbia, Vancouver 8, B.C., Canada, and University of Edinburgh
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In this note we construct certain Hilbert subspaces with Hilbert–Schmidt imbedding, for an arbitrary proper functional Hilbert space which consists of holomorphic functions. This work extends results of Chapter III in [1] and has applications in the regularity problem for generalised eigenfunctions (in particular to Theorem 2 in [2]). For an exposition of reproducing kernels and Bergman's kernel function we refer to [4].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 13 , Issue 2 , September 1972 , pp. 102 - 106
Copyright
Copyright © Glasgow Mathematical Journal Trust 1972

References

REFERENCES

1.Gerlach, E., On spectral representation for selfadjoint operators. Expansion in generalized eigenelements, Ann. Inst. Fourier Grenoble, 15 (1965), 537–574.CrossRefGoogle Scholar
2.Gerlach, E., Mean value properties of generalised eigenfunctions, Proc. Edinburgh Math. Soc. (2) 17 (1970), 155–158.CrossRefGoogle Scholar
3.Kreǐn, S. G. and Petunin, Ju. I., Scales of Banach spaces (Russian), Uspehi Mat. Nauk 21 (1966), no. 2 (128), 89–168. [English translation in Russian Math. Surveys 21 (1966), no. 2, 85–159.]Google Scholar
4.Meschkowski, H., Hilbertsche Räume mit Kernfunktion (Berlin, 1962).CrossRefGoogle Scholar