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Spaces of holomorphic functions and Hilbert–Schmidt subspaces
Published online by Cambridge University Press: 18 May 2009
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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].
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- Copyright © Glasgow Mathematical Journal Trust 1972