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Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. DOI: 10.23671/VNC.2017.2.6505 On Splitting Polynomials with Coefficients from Commutative Banach Algebras
Pasenchuk A. E.
Vladikavkaz Mathematical Journal 2017. Vol. 19. Issue 2.
Abstract:
The problem of decomposition of polynomials with coefficients from a unital commutative Banach algebra into a product of polynomials with coefficients in the same algebra is considered. Sufficient conditions for the existence of such decomposition and its construction are indicated. Some applications in the theory of Toeplitz operators on a circle and a torus are given. In particular, the equivalent regularization for a twodimensional Toeplitz operator with a special symbol is derived. Equations generated by the corresponding Toeplitz operators in the spaces of measurable squareintegrable vectorvalued functions on the circle and measurable square summable functions are examined. This leads to the construction of equivalent regularizers for the described Toeplitz operators. The regularizer construction turns out to be equivalent to right canonical WienerHopf factorization of some matrix function built from the symbol in a case of vector functions. An equivalent regularizer is built in explicit form for a twodimensional Toeplitz operator with a special symbol.
Keywords: polynomial, commutative Banach algebra, decomposition of a polynomial, Toeplitz operator, regularization.
Language: Russian
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For citation: Pasenchuk A. E. On Decomposition of Polynomials with Coecients from Commutative Banach Algebras. Vladikavkazskij matematicheskij zhurnal [Vladikavkaz Math. J.], vol. 19, no. 1, pp. 1827. DOI 10.23671/VNC.2017.2.6505 ← Contents of issue 
 

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