Geodesic
Spaces of holomorphic functions and Hilbert–Schmidt subspaces
Glasgow mathematical journal, Tome 13 (1972) no. 2, pp. 102-106

Voir la notice de l'article provenant de la source Cambridge University Press

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]. 
Gerlach, Eberhard. Spaces of holomorphic functions and Hilbert–Schmidt subspaces. Glasgow mathematical journal, Tome 13 (1972) no. 2, pp. 102-106. doi: 10.1017/S0017089500001488
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[1] 1.Gerlach, E., On spectral representation for selfadjoint operators. Expansion in generalized eigenelements, Ann. Inst. Fourier Grenoble, 15 (1965), 537–574. Google Scholar | DOI

[2] 2.Gerlach, E., Mean value properties of generalised eigenfunctions, Proc. Edinburgh Math. Soc. (2) 17 (1970), 155–158. Google Scholar | DOI

[3] 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] 4.Meschkowski, H., Hilbertsche Räume mit Kernfunktion (Berlin, 1962). Google Scholar | DOI

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