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Information × Registration Number 0220U100366, 0119U103204 , R & D reports Title Investigation of symmetric functions on some Banach spaces popup.stage_title Head Vasylyshyn Taras V., Кандидат фізико-математичних наук Registration Date 16-01-2020 Organization Vasyl Stefanyk Precarpathian National University popup.description2 The aim of the work is to construct algebraic bases of algebras of symmetric polynomials and to investigate spectra of algebras of symmetric analytic functions on some Banach spaces. It is described an algebraic basis of the algebra of all continuous symmetric polynomials on the Cartesian power of the complex Banach space of all complex-valued Lebesgue measurable essentially bounded functions on the segment, namely, it is proved that the so-called power sum elementary symmetric polynomials are algebraically independent and every continuous symmetric polynomial on the Cartesian power of the complex Banach space of all complex-valued Lebesgue measurable essentially bounded functions on the segment can be uniquely represented as an algebraic combination of the power sum elementary symmetric polynomials. It is investigated some properties of algebras of analytic functions generated by a sequence of polynomials on a complex Banach space. In particular, it is proved the formula for evaluation of the radius-function of a linear continuous functional on a subalgebra of the Frechet algebra of entire functions of bounded type on a complex Banach space, generated by a sequence of algebraically independent polynomials. It is described the spectrum of such a subalgebra of functions on the space of all bounded sequences of complex numbers. Also it is proved an algebraic basis of the algebra of all continuous symmetric polynomials on the direct sum of the space of all bounded sequences of complex numbers and of the space of all absolutely summable sequences of complex numbers. Product Description popup.authors Halushchak Svitlana I. Kravtsiv Victoria V. Pryimak Halyna M. popup.nrat_date 2020-04-02 Close