полнота

Finite Integral Transformations Method — Generalization of Classic Procedure for Eigenvector Decomposition

Authors: Senitsky Y. E.

The structural algorithm of the finite integral transformation method is presented as a generalization of the classical procedure of eigenvector decomposition. The initial-boundary problems described with a hyperbolic system of linear partial second order differential equations are considered. The general case of non-self adjoint solution by expansion in the vector-functions is possible only by the use of biorthogonal of finite integral transformations.

Affine System of Walsh Type. Completeness and Minimality

Authors: Al-Jourany K. H., Mironov V. A., Terekhin P. A.

The question on completeness and minimality of Walsh affine systems is considered. On the basis of functional-analytical structure of multishift in Hilbert space, which being the generalized analogue of the operator of simple one-side shift and closely connected with Cuntz algebra representations, we give definition of Walsh affine system. Various criteria and tests of completeness of affine systems of functions are established. A biorthogonal conjugate system is found and its completeness is proved. 

Affine Systems of Walsh Type. Orthogonalization and Completion

Authors: Terekhin P. A.

The new notion of affine system of Walsh type is introduced and studied. We proved results about orthogonalization and completion of affine systems of Walsh type with preservation of structure of affine systems.