We study additive models built with trend filtering, ie, additive models whose components
are each regularized by the (discrete) total variation of their $ k $ th (discrete) derivative, for …

Let ¹pnº denote the orthonormal polynomials associated with a measure with compact
support on the real line. Let be regular in the sense of Stahl, Totik, and Ullmann, and I be a …

For the weight w satisfying w, w^-1 ∈ BMO (T) w, w-1∈ BMO (T), we prove the asymptotics
of {Φ _n (e^ i θ, w)\} Φ n (ei θ, w) in L^ p-π, π, 2\leqslant p< p_0 L p-π, π, 2⩽ p< p 0, where …

Estimates in various Lebesgue spaces L_s (G) L s (G), 1 ≤ s ≤ ∞ 1≤ s≤∞, are obtained
for the root functions of an operator which relates to the differential operation-u''+ p (x) u'+ q …

For the measures on the unit circle that are equal to the sum of Lebesgue measure and $ p $
point masses, we give an estimate on the size of the corresponding orthonormal …

We give a simple proof of a classical theorem by A. Máté, P. Nevai, and V. Totik on
asymptotic behavior of orthogonal polynomials on the unit circle. It is based on a new real …

Suppose that ν is a given positive measure on-1, 1, and that μ is another measure on the
real line, whose restriction to-1, 1 is ν. We show that one can bound the orthonormal …

The growth of polynomials orthogonal on the unit circle with respect to a weight w that satisfies
w,w^{-1}\in L^\infty( {T}}) - NASA/ADS Now on home page ads icon ads Enable full ADS view …

The conjecture by Steklov was solved negatively by Rakhmanov in 1979. His original proof
was based on the formula for orthogonal polynomial obtained by adding point masses to the …

DS Lubinsky, “On zeros, bounds, and asymptotics for orthogonal polynomials on the unit circle”,
Mat. Sb., 213:11 (2022), 31–49; Sb. Math., 213:11 (2022), 1512–1529 Sbornik: Mathematics …