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Preliminary Facts on Semi-boundedness of Forms and Operators

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Semi-bounded Partial Differential Operators

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 243))

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Abstract

Let us recall that, in the classical theory of Hilbert spaces, the class of symmetric operators A, semi-bounded below is selected by the inequality

$$(Au,u)\geqslant c\parallel u \parallel^2$$

valid for any u belonging to D(A), the domain of A \(A(c\in\mathbb{R})\).

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© 2014 Springer International Publishing Switzerland

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Cialdea, A., Maz’ya, V. (2014). Preliminary Facts on Semi-boundedness of Forms and Operators. In: Semi-bounded Partial Differential Operators. Operator Theory: Advances and Applications, vol 243. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-04558-0_1

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