Displaying similar documents to “On the Paley-Wiener-Schwartz isomorphism in Hilbert spaces”

Some embedding properties of Hilbert subspaces in topological vector spaces

Eberhard Gerlach (1971)

Annales de l'institut Fourier

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A general theorem on Hilbert subspaces of dually nuclear spaces is proved, from which all previous results of K. Maurin and the writer on regularity of generalized eigenfunctions follow as simple corollaries. In addition some supplements to L. Schwartz’s work on Hilbert subspaces in spaces of smooth functions are given.

Structure of spaces of germs of holomorphic functions.

Nguyen Van Khue, P. Thien Danh (1997)

Publicacions Matemàtiques

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Let E be a Frechet (resp. Frechet-Hilbert) space. It is shown that E ∈ (Ω) (resp. E ∈ (DN)) if and only if [H(O)]' ∈ (Ω) (resp. [H(O)]' ∈ (DN)). Moreover it is also shown that E ∈ (DN) if and only if H(E') ∈ (DN). In the nuclear case these results were proved by Meise and Vogt [2].

Unsolved Problems

N. Aronszajn, L. Gross, S. Kwapień, N. Nielsen, A. Pełczyński, A. Pietsch, L. Schwartz, P. Saphar, S. Chevet, R. Dudley, D. Garling, N. Kalton, B. Mitjagin, S. Rolewicz, E. Schock, J. Daleckiĭ, J. Dobrakov, B. Gelbaum, G. Henkin, L. Nachbin, N. Peck, L. Waelbroeck, P. Porcelli, M. Rao, M. Zerner, V. Zakharjuta (1970)

Studia Mathematica

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1. The operator ideals and measures in linear spaces 469-472 2. Schauder bases and linear topological invariants 473-478 3. Various problems 479-483