Naslov
Oscillations of chirp-like functions

Autori
Korkut, Luka ; Resman, Maja

Izvornik
Georgian mathematical journal (1072-947X) 19 (2012), 4; 705-720

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Box dimension; chirp-like functions; oscillatory dimension; fractal oscillatority; p-clothoid.

Sažetak
Abstract. In this paper we deal with real oscillatory functions of the form y(x)=p(x)S(x) where p(x)\thilda x^\a, q(x) \thilda x^{; ; ; -\b}; ; ; as x \to 0 and S(t) is periodic. We impose some sufficient conditions on functions p, q and S which imply the d -dimensional fractal oscillatority of the function y(x) with d =2-(\a+1)/(\b+1), 0<\a<\b, thus extending a result of Tricot (1995). Using the obtained results, we show that the oscillatory dimension of both component functions of the p-clothoid is equal to d=(p+2)(p+1), where p > 1, and that the corresponding reflected functions are-dimensional fractal oscillatory. The case where p>2 was treated previously by Korkut et al. (2008, 2009).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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