CONVERGENCE OF DOUBLE LAGUERRE SERIES

L1-convergence of complex double Fourier series

It is proved that the complex double Fourier series of an integrable function f (x,y) with coefficients {c jk} satisfying certain conditions, will converge in L 1norm. The conditions used here are the combinations of Tauberian condition of Hardy– Karamata kind and its limiting case. This paper extends the result of Bray [1] to complex double Fourier series.

Uniform Convergence of Double Trigonometric Series

It is a classical problem in Fourier analysis to give conditions for a single sine or cosine series to be uniformly convergent. Several authors gave conditions for this problem supposing that the coefficients are monotone, non-negative or more recently, general monotone. There are also results for the regular convergence of double sine series to be uniform in case the coefficients are monotone ...

Counting Words with Laguerre Series

We develop a method for counting words subject to various restrictions by finding a combinatorial interpretation for a product of weighted sums of Laguerre polynomials with parameter α = −1. We describe how such a series can be computed by finding an appropriate ordinary generating function and applying a certain transformation. We use this technique to find the generating function for the numb...

Convergence of Double Fourier Series and W -classes

The double Fourier series of functions of the generalized bounded variation class {n/ ln(n + 1)}∗BV are shown to be Pringsheim convergent everywhere. In a certain sense, this result cannot be improved. In general, functions of class Λ∗BV, defined here, have quadrant limits at every point and, for f ∈ Λ∗BV, there exist at most countable sets P and Q such that, for x / ∈ P and y / ∈ Q, f is conti...

Uniform convergence of single and double sine series and integrals