Consider a boundary-functional problem with transmission conditions for the ordinary differential-operator equation on
with boundary-functional conditions
and transmission conditions
where , at , at , are complex numbers , is a linear operator, and is a linear functional in the space .
The authors prove an isomorphism, coerciveness with respect to the spectral parameter, completeness and an Abel basis for a system of root functions. The obtained results in the article are new even in case of Sobolev spaces without weight.