On basicity of the degenerate trigonometric system with excess | Zendy

Aydin Sh. Shukurov | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

On basicity of the degenerate trigonometric system with excess

Author(s) -

Aydin Sh. Shukurov

Publication year - 2017

Publication title -

acta et commentationes universitatis tartuensis de mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.276

H-Index - 6

eISSN - 2228-4699

pISSN - 1406-2283

DOI - 10.12697/acutm.2017.21.17

Subject(s) - sine , trigonometric functions , mathematics , degenerate energy levels , trigonometry , completeness (order theory) , schauder basis , pure mathematics , differentiation of trigonometric functions , basis (linear algebra) , function (biology) , exponential function , mathematical analysis , discrete mathematics , physics , geometry , quantum mechanics , evolutionary biology , linear interpolation , polynomial , banach space , bicubic interpolation , biology

The basis properties (completeness,minimality and Schauder basicity) of systems of the form {omega(t)phi(n)(t)}, where {phi(n)(t)} is an exponential or trigonometric (cosine or sine) systems, have been investigated in several papers. Concrete examples of the weight function omega(t) are known for which the system itself is not complete and minimal but has excess becomes complete and minimal in corresponding L-p space only after elimination of some of its elements. The aim of this paper is to show that if omega(t) is any measurable weight function such that the system {omega(t) sin nt}(n epsilon N) has excess, then neither this system itself, nor a system obtained from it by elimination of an element, is not a Schauder basis.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research