 0790 Vladimir Ryzhov
 A General Boundary Value Problem and its Weyl Function
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Apr 14, 07

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Abstract. We study the abstract boundary value problem defined in terms
of the Green identity and introduce the concept of Weyl
operator function M( ) that agrees with other definitions
found in the current literature. In typical cases of
problems arising from the multidimensional partial equations
of mathematical physics the function M( ) takes values in
the set of unbounded densely defined operators acting on
the auxiliary boundary space. Exact formulae are obtained
and essential properties of M( ) are studied. In particular,
we consider boundary problems defined by various boundary
conditions and justify the well known procedure that reduces
such problems to the "equation on the boundary" involving
the Weyl function, prove an analogue of the BorgLevinson
theorem, and link our results to the classical theory of
extensions of symmetric operators.
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