Ukrainian Mathematical Bulletin

Volume 1, Issue 1, 2004 pp. 77-105.

Abstract Green Formula for a Triple of Hilbert Spaces, Abstract Boundary-Value and Spectral Problems

Authors: N.D.Kopachevsky, S.G.Krein
Author institution: Taurida National V.Vernadsky University

Summary: For a triple of Hilbert spaces related to one another in a certain way and for an abstract trace operator, we deduce an abstract Green formula that generalizes the well-known Green formula for the Laplace operator. Using this formula, we investigate abstract Dirichlet, Neumann, and Newton boundary-value problems and the corresponding spectral problems.

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