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

Autori
Perić, Ivan

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Conference on Inequalities and Applications '07 / Pales, Zsolt ; Gilanyi, Attila - Deberecen : Institute of Mathematica, University of Debrecen, 2007, 66-66

Skup
Conference on Inequalities and Applications '07

Mjesto i datum
Noszvaj, Mađarska, 09.09.2007. - 15.09.2007

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Euler-type identities; quadratic formulae; frequency

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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