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 …

Computing the Jacobian of the solution of an optimization problem is a central problem in
machine learning, with applications in hyperparameter optimization, meta-learning …

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

The aim here is to consider the orthogonal polynomials S n (ν 0, ν 1, s; x) S_n(ν_0,ν_1,s;x)
with respect to an inner product of the type⟨ f, g⟩ s=∫ f (x) g (x) d ν 0 (x)+ s∫ f′(x) g′(x) d …

In this work, we deal in ad dimensional unit ball equipped with an inner product constructed
by adding a mass point at zero to the classical ball inner product applied to the gradients of …

Given a pair of quasi-definite moment functionals {v 0, v 1} we introduce the concept of
coherence of the second kind in terms of an algebraic relation that the corresponding …

In this paper, Geronimus transformations for matrix orthogonal polynomials in the real line
are studied. The orthogonality is understood in a broad sense, and is given in terms of a …

Let u be a moment functional associated with the Hermite, Laguerre, or Jacobi classical
orthogonal polynomials. We study approximation by polynomials in H r (u), the Sobolev …

One-step estimation of differentiable Hilbert-valued parameters Page 1 The Annals of Statistics
2024, Vol. 52, No. 4, 1534–1563 https://doi.org/10.1214/24-AOS2403 © Institute of …

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