Note on some characteristic properties of functions of the second kind
Notes on a family of Riordan arrays and associated integer Hankel transforms.
O aproximací obrazu v Hilbertově transformací ortogonálními řadami racionálních lomených funkcí
On 2-orthogonal polynomials of Laguerre type.
On a class of generalized Laguerre's polynomials
On A Fourth Order Wronskian Associated With Classical Orthogonal Polynomials
On a fourth order Wronskian associated with classical orthogonal polynomials.
On a positive sine sum
On a Szegö's theorem of orthogonal polynomials.
It is found that the asymptotical density of zeros of a system of orthogonal polynomials whose weight function belongs to a wide class of distribution functions has the expression ρ(x) = π-1 (1 - x2)-1/2. This result is shown in two completely different ways: (1) from a Szegö theorem and (2) from a Geronimus theorem and a finding recently obtained by the author in a context of Jacobi matrices.
On -summability of orthogonal series
In the paper, we prove two theorems on summability, , of orthogonal series. Several known and new results are also deduced as corollaries of the main results.
On block recursions, Askey's sieved Jacobi polynomials and two related systems
Two systems of sieved Jacobi polynomials introduced by R. Askey are considered. Their orthogonality measures are determined via the theory of blocks of recurrence relations, circumventing any resort to properties of the Askey-Wilson polynomials. The connection with polynomial mappings is examined. Some naturally related systems are also dealt with and a simple procedure to compute their orthogonality measures is devised which seems to be applicable in many other instances.
On convergence of orthonormal expansions for exponential weights.
On Fourier series of Jacobi-Sobolev orthogonal polynomials.
On generalized Jacobi matrices and orthogonal polynomials.
On group decompositions of bounded cosine sequences
A two-sided sequence with values in a complex unital Banach algebra is a cosine sequence if it satisfies for any n,m ∈ ℤ with c₀ equal to the unity of the algebra. A cosine sequence is bounded if . A (bounded) group decomposition for a cosine sequence is a representation of c as for every n ∈ ℤ, where b is an invertible element of the algebra (satisfying , respectively). It is known that every bounded cosine sequence possesses a universally defined group decomposition, here referred...
On the asymptotic behaviour of some sequences of polynomials generated by second order linear recurrence relations.
On the best constants in the Khinchin inequality
On the constant in Meńshov-Rademacher inequality.
On the distributional orthogonality of the general Pollaczek polynomials.
On the Krall-type polynomials.