TY  - JOUR
ID  - Ryzhov2007
LB  - Ryzhov2007
AU  - Ryzhov, Vladimir
TI  - A general boundary value problem and its Weyl function
ST  - A general boundary value problem and its Weyl function
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2007
VL  - 27
IS  - 2
SP  - 305
EP  - 331
DO  - http://dx.doi.org/10.7494/OpMath.2007.27.2.305
UR  - http://dx.doi.org/10.7494/OpMath.2007.27.2.305
AB  - We study the abstract boundary value problem defined in terms of the Green identity and introduce the concept of Weyl operator function \(M(\cdot)\) 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 \(M(\cdot)\) takes values in the set of unbounded densely defined operators acting on the auxiliary boundary space. Exact formulae are obtained and essential properties of \(M(\cdot)\) 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 Borg-Levinson theorem, and link our results to the classical theory of extensions of symmetric operators
KW  - abstract boundary value problem
KW  - symmetric operators
KW  - Green formula
KW  - Weyl function
SN  - 1232-9274
ER  -