The analysis of orthogonal polynomials associated with general weights was a major theme
in classical analysis in the twentieth century, and undoubtedly will continue to grow in …

Analytic aspects of Sobolev orthogonal polynomials revisited - ScienceDirect Skip to main
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Abstract Systems of functions are considered which are associated with a given orthogonal
system and are orthogonal with respect to an inner product of Sobolev type involving terms …

В ряде наших работ [1]–[5] были введены так называемые смешанные ряды по
классическим ортогональным полиномам, частичные суммы которых обладают …

We study the sequence of monic polynomials {S n} n⩾ 0, orthogonal with respect to the
Jacobi-Sobolev inner product〈 f, g〉 s=∫− 1 1 f (x) g (x) d μ α, β (x)+∑ j= 1 N∑ k= 0 dj λ j, kf …

Strong asymptotics for the sequence of monic polynomialsQn (z), orthogonal with respect to
the inner product (f, g) S=∫ f (x) g (x) dμ 1 (x)+ λ∫ f′(x) g′(x) dμ 2 (x), λ> 0, withzoutside of …

For every system of functions $\{\varphi_k (x)\} $ which is orthonormal on $(a, b) $ with
weight $\rho (x) $ and every positive integer $ r $ we construct a new associated system of …

Ratio and relative asymptotics are given for sequences of polynomials orthogonal with
respect to measures supported on an arc of the unit circle, where their absolutely continuous …

Let μ be a finite positive Borel measure supported in [− 1, 1] and introduce the discrete
Sobolev-type inner product [Formula: see text] where the mass points ak belong to [− 1, 1], M …

Рассмотрены системы функций, которые являются ортогональными относительно
скалярных произведений типа Соболева, содержащих слагаемые с массами …