On a class of generalized Laguerre's polynomials
On a Fourier-Bessel series of special kind
On A Fourth Order Wronskian Associated With Classical Orthogonal Polynomials
On a fourth order Wronskian associated with classical orthogonal polynomials.
On a gap series of Mark Kac
Mark Kac gave an example of a function f on the unit interval such that f cannot be written as f(t)=g(2t)-g(t) with an integrable function g, but the limiting variance of vanishes. It is proved that there is no measurable g such that f(t)=g(2t)-g(t). It is also proved that there is a non-measurable g which satisfies this equality.
On a generalization of the martingale maximal theorem
On a non-self adjoint eigenfunction expansion.
On a non-self adjoint expansion formula.
On a positive sine sum
On a property of continuous solutions of the dilation equation with positive coefficients
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 a Theorem of Ingham.
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 a.e. convergence of expansion with respect to a bounded orthonormal system of polygonals
On almost everywhere and mean convergence of Hermite and Laguerre expansions
On an approximation of function and its derivatives.
On analytic rapidly decreasing functions of a real variable
Condizione necessaria e sufficiente affinché una funzione rapidamente decrescente di variabile reale sia uniformemente analitica è che per i suoi coefficienti di Fourier-Hermite riesca per abbastanza piccolo.
On Approximation Of Continuous And Differentiable Functions By Fourier-Jacobi Series
On bases and unconditional bases in the spaces ,1≤p<∞
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.