Displaying similar documents to “Ordered analytic Hilbert spaces over the unit disk”

Hilbert spaces of analytic functions of infinitely many variables

O. V. Lopushansky, A. V. Zagorodnyuk (2003)

Annales Polonici Mathematici

Similarity:

We study spaces of analytic functions generated by homogeneous polynomials from the dual space to the symmetric Hilbertian tensor product of a Hilbert space. In particular, we introduce an analogue of the classical Hardy space H² on the Hilbert unit ball and investigate spectral decomposition of unitary operators on this space. Also we prove a Wiener-type theorem for an algebra of analytic functions on the Hilbert unit ball.

Some embedding properties of Hilbert subspaces in topological vector spaces

Eberhard Gerlach (1971)

Annales de l'institut Fourier

Similarity:

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.

On the analyticity of generalized eigenfunctions (case of real variables)

Eberhard Gerlach (1968)

Annales de l'institut Fourier

Similarity:

On démontre que, dans les espaces fonctionnels propres de Hilbert (avec un noyau reproduisant), formés de fonctions analytiques de n variables dans un domaine G , pour tout opérateur auto-adjoint, les fonctions propres généralisées sont des fonctions réelles-analytiques dans G .