Goriunov A. One-dimensional differential operators with distribution coefficients

Quasi-differential operators theory and its application to some classes of differential operators with distributional coefficients, namely Sturm-Liouville operators and binomial operators of the higher order are investigated in the thesis. Sufficient conditions for the uniform resolvent approximation of quasi-differential operators are established.The parametrical bijective continuous parametrization of all self-adjoint, maximal dissipative and maximal accumulative extensions and generalised resolvents of these operators is found. Due to regularization by means of Shin-Zettl quasi-derivatives differential operators with distributional coefficients are defined as quasi-differential. On the basis of results obtained sufficient conditions for the uniform resolvent approximation of Sturm-Liouville operators and differential binomial operators of the higher order with distributional coefficients are established. The parametrical bijective continuous parametrization of all self-adjoint, maximal dissipative and maximal accumulative extensions and generalised resolvents of these operators is found.