The quantized Jacobi polynomials
The author studies a system of polynomials orthogonal at a finite set of points its weight approximating that of the orthogonal system of classical Jacobi polynomials.
The restricted Toda chain, exponential Riordan arrays, and Hankel transforms.
The second-order self-associated orthogonal sequences.
The symmetrical -semiclassical orthogonal polynomials of class one.
The -variants of a prescribed sequence of orthogonal polynomials.
Three cases of normality of Hessenberg's matrix related with atomic complex distributions.
Toeplitz Arrays, Linear Sequence Transformations and Orthogonal Polynomials.
Über orthonormale Polynome und ein assoziiertes Momentenproblem.
Uniform asymptotics for orthogonal polynomials.
Weak type (1,1) estimates of the maximal function for the Laguerre semigroup in finite dimensions.
We prove that, in arbitrary finite dimensions, the maximal operator for the Laguerre semigroup is of weak type (1,1). This extends Muckenhoupt's one-dimensional result.
What is a Sobolev space for the Laguerre function systems?
We discuss the concept of Sobolev space associated to the Laguerre operator , y ∈ (0,∞). We show that the natural definition does not agree with the concept of potential space defined via the potentials . An appropriate Laguerre-Sobolev space is defined in order to achieve that coincidence. An application is given to the almost everywhere convergence of solutions of the Schrödinger equation. Other Laguerre operators are also considered.
Widom factors for the Hilbert norm
Given a probability measure μ with non-polar compact support K, we define the n-th Widom factor W²ₙ(μ) as the ratio of the Hilbert norm of the monic n-th orthogonal polynomial and the n-th power of the logarithmic capacity of K. If μ is regular in the Stahl-Totik sense then the sequence has subexponential growth. For measures from the Szegő class on [-1,1] this sequence converges to some proper value. We calculate the corresponding limit for the measure that generates the Jacobi polynomials, analyze...
Zero distribution of sequences of classical orthogonal polynomials.
Zero distributions via orthogonality
We develop a new method to prove asymptotic zero distribution for different kinds of orthogonal polynomials. The method directly uses the orthogonality relations. We illustrate the procedure in four cases: classical orthogonality, non-Hermitian orthogonality, orthogonality in rational approximation of Markov functions and its non- Hermitian variant.
Асимптотика полиномов совместной ортогональности в случае Анджелеско
Асимптотические свойства многочленов, ортогональных на системе контуров, и периодические движения цепочек Тода
Асимптотическое поведение ортогональных многочленов
Биортогональные системы рациональных функций и наилучшее приближение ядра Коши на вещественной оси
Локализация теорем равносходимости
О возможной скорости роста многочленов, ортогональных с непрерывным положительным весом