Approximation of unbounded functionals by the bounded ones in Hilbert space

V.F. Babenko; R.O. Bilichenko

doi:10.15421/241201

Approximation of unbounded functionals by the bounded ones in Hilbert space

V.F. Babenko (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0001-6677-1914
R.O. Bilichenko (Oles Honchar Dnipropetrovsk National University)

Abstract

We obtained the value of the best approximation of unbounded functional $$$F_f(x) = (A^kx, f)$$$ on the class $$$\{ x\in D(A^r) \colon \| A^r x \| \leqslant 1 \}$$$ by linear bounded functionals ($$$A$$$ is a self-adjoint operator in the Hilbert space $$$H$$$, $$$f\in H$$$, $$$k < r$$$).

Keywords

functional; self-adjoint operator; Hilbert space

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