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Some extremal functions in fourier analysis pdf

 
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MessagePosté le: Mer 14 Fév - 16:50 (2018)    Sujet du message: Some extremal functions in fourier analysis pdf Répondre en citant

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18 Mar 2009 is minimized. A typical variant of this problem occurs when we impose the additional condition that K(z) is real on R and satisfies K(x) ? f (x) for all x ? R. In this case a minimizer of the integral (1.1) is called an extremal majorant of f (x). Extremal minorants are defined analogously. The study of these
23 Sep 2008 Abstract: We obtain extremal majorants and minorants of exponential type for a class of even functions on $\R$ which includes and , where . We also give periodic versions of these results in which the majorants and minorants are trigonometric polynomials of bounded degree. As applications we obtain
30 Nov 2013 [19] Mikosch, T. and Zhao, Y. (2013) A Fourier analysis of extreme events. . certain order. This thesis is located at the boundary beetwen time series analysis and extreme value theory. In the latter field one is particularly from the sequence of the indicator functions of the extreme events in a time series.
20 Dec 2017 Some Extremal Functi | We obtain the best approximation in $L^1(\R)$, by entire functions of exponential type, for a class of even functions that includes $e^{-\lambda|x|}$, where $\lambda >0$, $\log |x|$ and $|x|^{\alpha}$, where $-1 < \alpha < 1$. We also give periodic versions of these results where
S 0002-9947(2010)04886-X. Article electronically published on June 9, 2010. SOME EXTREMAL FUNCTIONS IN FOURIER ANALYSIS. II. EMANUEL CARNEIRO AND JEFFREY D. VAALER. Abstract. We obtain extremal majorants and minorants of exponential type for a class of even functions on R which includes log |x|
Abstract. This is a preliminary report about a work that is still in progress. We begin with a brief introduction to some extremal functions in Fourier analysis, such as Beurling's and Selberg's, and others obtained from solving certain problems of interpolation of given functions at points of the form n+? for some fix ?1. 2 < ? ? 1.
Full-text PDF Free Access [GV1] S. W. Graham and J. D. Vaaler, Extremal functions for the Fourier transform and the large sieve, Topics in Classical Number Theory (G. Halasz, ed.) [Zo2] V. M. Zolotarev, Some inequalities in probability theory and their application in sharpening the Lyapunov theorem, Soviet Math. Dokl.
Citation. Vaaler, Jeffrey D. Some extremal functions in Fourier analysis. Bull. Amer. Math. Soc. (N.S.) 12 (1985), no. 2, 183--216.https://projecteuclid.org/euclid.bams/1183552525
CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We obtain extremal majorants and minorants of exponential type for a class of even functions on R which includes log |x | and |x | ?, where ?1 < ? < 1. Some extremal functions in Fourier analysis, II (2008). Cached. Download as a PDF
Volume 12, Number 2, April 1985. SOME EXTREMAL FUNCTIONS IN FOURIER ANALYSIS. BY JEFFREY D. VAALER1. 1. Introduction. In the late 1930s A. Beurling observed that the entire function. (1.1) B(z) = ( ^ ) 2 { t (z - n)-2 -. ?. (z - my2. + 2*"1} satisfies a simple and useful extremal property. We have. (1.2) sgn(x)<B(x).

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