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This monograph describes mathematical methods applicable to studying nonclassical problems of mathematical physics. The emphasis of the book is on applications of the interpolar theory of Banach spaces to the theory of linear operators to be expotentially dichotomous, to some continuity properties of linear operators in Hilbert scales, to the Riesz basis property of eigenelements and associated elements of linear pencils and the correspondending elliptic problems with indefinite weight functions, and to studying nonclassical boundary value problems for first order operator-differential equations.

Banach spaces. --- Interpolation spaces. --- Nonclassical mathematical logic. --- Operator theory. --- Banach Spaces. --- Boundary Value Problems. --- Continuity Properties. --- Dichotomous. --- Eigenelements. --- Elliptic Problems. --- Expotential. --- Hilbert Scales. --- Indefinite Weight Functions. --- Interpolar Theory. --- Linear Operators. --- Linear Pencils. --- Nonclassical. --- Operator-differential Equations. --- Riesz Basis Property.