4 papers
Remarkable properties of the functions and related integrals
Houry Melkonian, Shingo Takeuchi
Different types of sinc integrals are investigated when the standard sine function is replaced by the generalised in two parameters. A striking generalisation of the i…
Behaviour of norms of the $\sinc_{p}$ function
David E Edmunds, Houry Melkonian
An integral inequality due to Ball involves the norm of the $\sinc_p$ function; the dependence of this norm on as is now understood. By use of rece…
A multi-term basis criterion for families of dilated periodic functions
Lyonell Boulton, Houry Melkonian
In this paper we formulate a concrete method for determining whether a system of dilated periodic functions forms a Riesz basis in . This method relies on a general frame…
Generalised cosine functions, basis and regularity properties
Lyonell Boulton, Houry Melkonian
We examine regularity and basis properties of the family of rescaled -cosine functions. We find sharp estimates for their Fourier coefficients. We then determine two thresholds,…