Rotationally Symmetric Lacunary Functions and Products of Centered Polygonal Lacunary Functions

Lacunary Partition Functions

We combine the theory of Bailey chains and the theory of binary quadratic forms to show that there are large classes of q-series which are not theta series but whose coefficients are almost all 0. We interpret some examples in terms of simple partition functions.

Problems on Averages and Lacunary Maximal Functions

We prove three results concerning convolution operators and lacunary maximal functions associated to dilates of measures. First we obtain an H to L bound for lacunary maximal operators under a dimensional assumption on the underlying measure and an assumption on an Lp regularity bound for some p > 1. Secondly, we obtain a necessary and sufficient condition for L boundedness of lacunary maximal ...

Metric number theory, lacunary series and systems of dilated functions

Approximation of Continuous Functions by Means of Lacunary Polynomials

be the orthonormal trigonometric sums on Di for weight p(6)cr(0) ; if the u's and v's are uniformly bounded on a point set D2 contained in Di, the same is true of the U's and Vs. For this case the proof admits a materially simpler formulation than when geometric configurations are contemplated having the degree of generality previously considered. The details relating to the loci C', C", K, K',...

Some Spaces of Lacunary Convergent Sequences Defined by Orlicz Functions

We introduce the sequence spaces [ ˆ w(M)] and [ ˆ w(M)] θ of strong almost convergence and lacunary strong almost convergence respectively defined by the Orlicz function M. We establish certain inclusion relations and show that the above spaces are same for any bounded sequences. 1. Definitions and notations A sequence x ∈ l ∞ , the space of bounded sequences x = (x k), is said to be almost co...