Cite this article as:

Al-Jourany K. H., Mironov V. A., Terekhin P. A. Affine System of Walsh Type. Completeness and Minimality. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2016, vol. 16, iss. 3, pp. 247-256. DOI: https://doi.org/10.18500/1816-9791-2016-16-3-247-256


Language: 
Russian
Heading: 
UDC: 
517.51

Affine System of Walsh Type. Completeness and Minimality

Abstract: 

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. 

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