Some problems of the spectral theory of a second-order differential equation with a variable unbounded operator coefficient

V. M. Bruk

Ul'yanovsk Pedagogical Institute

Abstract: A self-adjoint second-order differential expression with an unbounded operator coefficient is considered in the space of vector functions. The domain of definition of the minimum and maximum operators generated by this expression is investigated, it is shown that any generalized resolvent of the minimum operator is an integral operator, and expansion in eigenfunctions is performed.

UDC: 513.88

Received: 20.11.1973

 English version: Mathematical Notes, 1974, 16:5, 1079–1084

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