Subsymmetric Polynomials on Banach Spaces and Their Applications

Vitalii Bihun, Daryna Dolishniak, Viktoriia Kravtsiv and Andriy Zagorodnuyk ()
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Vitalii Bihun: Faculty of Mathematics and Computer Science, Vasyl Stefanyk Carpathian National University, 57 Shevchenka Str., 76018 Ivano-Frankivsk, Ukraine
Daryna Dolishniak: Faculty of Mathematics and Computer Science, Vasyl Stefanyk Carpathian National University, 57 Shevchenka Str., 76018 Ivano-Frankivsk, Ukraine
Viktoriia Kravtsiv: Faculty of Mathematics and Computer Science, Vasyl Stefanyk Carpathian National University, 57 Shevchenka Str., 76018 Ivano-Frankivsk, Ukraine
Andriy Zagorodnuyk: Faculty of Mathematics and Computer Science, Vasyl Stefanyk Carpathian National University, 57 Shevchenka Str., 76018 Ivano-Frankivsk, Ukraine

Mathematics, 2025, vol. 13, issue 22, 1-30

Abstract: We investigate algebraic and topological properties of subsymmetric polynomials on finite- and infinite-dimensional spaces. In particular, we focus on the problem of the existence of an algebraic basis in the algebra of subsymmetric polynomials, as well as possible extensions of subsymmetric polynomials and analytic functions to larger spaces. We consider algebras of subsymmetric analytic functions of bounded type and their spectra, and study linear subspaces in the zero-sets of subsymmetric polynomials, as well as subspaces where a subsymmetric polynomial is symmetric. In addition, we propose some possible applications of subsymmetric polynomials in cryptography and in operator theory.

Keywords: symmetric polynomials; subsymmetric polynomials on Banach spaces; algebraic basis of polynomials; spectrum of algebra; extension of polynomials; subsymmetric analytic functions; polynomial hash function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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