Error estimates of quadrature formulas for classes of functions with bounded mixed derivative (Q804221)

The author investigates quadrature formulae for functions in two real variables. These functions are supposed to be \(2\pi\)-periodic in each variable and, moreover, they have some special representation by trigonometric polynomials. The asymptotic behaviour of the quadrature formulae is established in two theorems. Their proofs are based on several works of N. S. Bakhvalov. It is also shown that quadrature formulae constructed on the basis of the Fibonacci sequence are in some sense universal.