Orthonormal polynomial bases in function spaces
Copyright policy )Orthonormal polynomial bases in function spaces
Let \(\Phi=(\Phi_ k)_{k=0}^ \infty\) be an orthonormal system of trigonometric polynomials on the unit circle \(T\) and let \(v_ n=\max_{k\leq n}\deg\Phi_ k\). The main problem consists in estimating the sequence \((v_ n)\) from above. It is shown by construction that there exists a system \(\Phi\) such that \(v_ n\leq{4\over 3}n\), and \(\Phi\) is a Schauder basis in \(C(T)\) (also in \(L_ 1(T))\), and an unconditional basis in \(\text{Re} H_ 1\) (also in \(L_ p(T)\) for \(1
- Institute of Mathematics Poland
- Polish Academy of Sciences Poland
- Polish Academy of Learning Poland
unconditional basis, Schauder basis, Trigonometric approximation, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, orthonormal system of trigonometric polynomials on the unit circle
unconditional basis, Schauder basis, Trigonometric approximation, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, orthonormal system of trigonometric polynomials on the unit circle
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