engleski

Frequency variant of Euler type identities and the problem of sign constancy of the kernel in associated quadrature formulas

Extended Euler identities generalize the well known formula for the expansion of an function in Bernoulli polynomials. Quadrature formulas are obtained using affine combinations of the extended Euler identities for symmetric nodes. The main step in obtaining the best possible error estimates is to prove that in this manner obtained kernel has some "nice" zeroes. Generally, the problem of distribution of nodes such that this kernel has controlled zeroes it seems to be difficult. Based on Multiplication Theorem the frequency variants of the extended Euler identities are given. Analogously obtained kernel appears to be more tractable for the investigation of zeroes. The case of m-adic frequencies and the case of frequencies with no gaps are completely solved. The general case is considered using some interesting convexity arguments.

Euler-type identities; quadratic formulae; frequency

nije evidentirano