Twentieth Hilbert problem. Generalized solutions of operator equations

Among the 23 problems of D. Hilbert, which this great mathematician formulated in 1900 at the International Congress of Mathematics in Paris as a testament to future generations of mathematicians, a decent place occupies a twentieth problem - "The overall task of boundary conditions", which raises the problem of expanding the classical concept of solving and Development of the concept of a generalized solution of the operator equation.
The final solution to this problem does not exist. However, the presence of many different definitions of generalized decisions currently exercising today, and obvious analogies between them suggest that there is a certain overall design approach to the construction of the concept of generalized solvability. Search for this approach and dedicated to this book