navbar-top.gif
btn_spacer.gifHomeTopicsLatestRandomAboutFAQsParticipateAuthoring Areabtn_spacer.gif

Extremal Trigonometric Polynomials

Consider the trigonometric polynomial of degree such that not all of the and are zero. Babenko's theorem (1984) states that the measure of the subset of for which is at least . The unique extremal polynomial, positive exactly on the interval and normalized so that , is constructed and shown for small values of .


The extremal polynomial shown is .
Its zeros are located at . All the zeros are double except those at .
H. L. Montgomery and U. M. A. Vorhauer, "Biased Trigonometric Polynomials," The American Mathematical Monthly, 114(9), 2007 pp. 804–808.
Additonal information can be found at Wikipedia.
Powered by Wolfram Mathematica
Give us your feedback
Give us your feedback

Source page:




 often  occasionally  never

Note: Please do not include anything you consider confidential or proprietary. We will keep your information private. We will not give it to any third party.
Privacy Policy »

©  2008 The Wolfram Demonstrations Project & Contributors    Wolfram Research    Site Index    Terms of Use    Privacy Policy    RSS    Atom